Allow me to quickly make a first point of clarification. While we normally talk about cinema in terms of their "narrative structure", the level of conceptual specificity that Deleuze invokes in these books requires that we make crucial distinctions between the notion of connection of images and "narrative". As a story-telling species, language naturally forms the basis of how we present or represent experience. But it overshadows what lies beneath, which are "images". All of life responds first and foremost to signs, from the most basic to the most advanced. And more importantly as relates to Deleuze's concern for understanding the potentiation of thought, images have a primary relationship with thought, not language. Language works on top of, side-by-side with and through them, for humans. From the pespective of the experience of the brain, the association or connection images and "narratives" are not at all synymous. The brain experiences all sorts of way more complex and multicomponential forms of expression/content, and so do our representations of them. But I only mention this so that the way you understand everything else isn't reduced to that idea of "narrativization".
Now, to your questions. Before one can understand what a "crystal" is, lets first situate what is actually being discussed in these books. He's talking about the advent of moving images and advanced cinematography almost anthropologically. Dissecting objects and signs of experience in general insofar as we represent them to ourselves in forms of human expression (as a form of art that mimicks natural perception). All of this sounds odd and very strange philosophically until we retrace the source of inspiration of the discussion, which comes from Bergson and his connection of 'mobile section' and 'abstract time' as one sees in this art form, to Zeno, who played a big role in both of Bergson's theses insofar as he tackled the notions of spatiality/temporality.
So the object is not cinema, but human experience (under the very broad distinctions of sensory-motor schema--movement-- and time). But why cinema and not simply talk about movement and time in general? For two reasons, 1) because human experience is not general, it's real, it's concrete, and it's how your brain receives and participates in the unfolding of time, so there's a richness in the exposition of cases that is simply not generalizable in terms of effects and affects vis a vis subjects; and 2) this gap between generalized transcendent conceptualizations and actual experience is precisely what explains the infinite diversity of what brains/bodies experience, the role of thought (and what contributes to the lack of thought) in human expreience, the proliferation of fictions, the manipulation of subjects of experience, the production and manipulation of affects, the production of subjectivity as a whole etc. All of this is involved both implicitly and explicitly in the discussions of movement-images and time-images in a high degree of nuanced categorizations and elaborations that take as their origin philosophical theses on movement and time. E.g. the Bergsonian theses that open Cinema 1:
- Movement is distinct from the space covered, where space covered is past, movement is present (or the act of covering). The space covered is infinitely divisible, but movement is indivisible, or cannot be divided without changing qualitatively each time it is divided. The spaces covered all belong to a single, identical, homogeneous space, while the movements are heterogeneous, irreducible among themselves. This entire point leads to the very important distinction Bergons makes between real movement (also known as concrete duration) and abstract time (which Bergson gives the nickname "cinematic time").
- The second thesis takes up this false time and divides it into two general historical kinds: a) the taking of priviledged (ideal) instants as eternal (or making movement from the priviledged instant; and b) the mechanical succession of instants or continuity of movement which gives the impression of real movement (a Whole) by accumulating generic instances.
- The third is the thesis that not only is an "instant" an immobile section of movement, but movement is a mobile section of duration, that is, of the Whole, or of a whole.
Cinema II poses theses that complement those of made on "movement" (and I can't enumerate them all here because it'll get very complicated and I don't want this post to be too long), the most important of which are that:
- Our actual existence, as it unfolds in time, duplicates itself along with a virtual existence, a mirror-image. Every moment of our life presents the two aspects, it is actual and virtual, perception on the one side and recollection on the other . . . Whoever becomes conscious of the continual duplicating of his present into perception and recollection ... will compare himself to an actor playing his part automatically, listening to himself and beholding himself playing.'; and
- If the virtual past is 'a single dimension in which all past events coexist', and each actual present has a virtual double, we can think of this as a cone, remembering that 'each present moment is a contraction of the past, the concentration of the entire cone in the point of its apex'. We locate ourselves in this virtual past and find there different planes of consciousness, cross sections of the cone or sheets of memories. On those sheets, there are some points with particular affective tones depicted with particular significance. (These are what in Mille Plateaux are depicted as geological layers or strata), each one with its '"tones,… aspects… singularities… brilliant points ... dominants". So, in the virtual past you have notions of a non-chronological time —the '"pre-existence of the past in general" (the cone as a whole), "the coexistence of all the sheets of the past" (the cross sections), and "the existence of a most contracted degree" (the apex)'. The virtual past therefore contains all the aspects of time —the dilated past, the contracted past, and the future projected past.
Between Virtual and Actual
While not going into the types of movement-images here, these images in general can be defined as ways of slicing up experience in contractions of mental experience. By movement one should understand a conception of matter that is flowing. Nothing is static in experience. Matters always flows. So a particular flow in experience can be of whatever undefined duration, but something cuts it, makes it distinct, the particular cut that define distinct duration instances are what can be described as the "images" in Cinema I. The three central types of movement image he defines are the perception-image, action-image, affection-image, all crucial because they neatly group any sub-categorizations of the subjects experience in time.
There are three basic time images as well, but they are distinguished from movement-images because they are images which are different from themselves, which are virtual to themselves, or which are infused with past/future. One could also say that they are distinguished from the more actual images of Cinema I in that we are always not fully what they are. That is to say that they are virtual, and function as signs (referring to other signs).
Lived time, or time that endures, flows (thus implicating the movement-imaging). As distinct from abstract time however (chronos), it is that in which the past and future penetrate into the present in the form of memory and desire. Time stretches when it seems to move more slowly (ie: when bored), and contracts during moments of crisis, or when we inter into moments of dreaming, fantasy, reverie, and more shallowly during moments of action. All three central sub-types of time-images are virtual in origin, ranging from the surface recognition in the virtual of the actual's passing, to inhabiting images of past as memory, tied to the actual but infusing it with blocks of pure past, and the most extreme which looses formal direct connection with the actual despite depending on it in general as material (the closes example one might "actually" experience being that of dream-states). Any image which functions to helps us recognize, recollect, or dream, is a type of time-image or time-cut/slice infusing into the present something not of itself actual. The key point to them however is that they infuse difference into the present. Whereas with movement images you have beginning, middle, end narratives. Time-images, whereever they appear change the significance of what was beginning, middle and end. It's not a simple issue of succession anymore, but all sorts of circuits that complicate a development.
So finally, what is a crystal?
If as in Bergson's temporal thesis, memory is not a current image that would be formed after the perceived object, but the virtual image that coexists with the actual perception of the object, then memory is the contemporary virtual image of the actual object, its double, its "image in the mirror." There is also a perpetual exchange between the actual object and its virtual image-- the virtual image does not cease becoming actual. The virtual image absorbs all the variation of signs at the same instant that these variations become little more than a virtuality. This perpetual exchange between the virtual and the actual is what defines a crystal. When you've reached a point of indiscernability between virtual and actual, you have a crystal.
If the actualization of the virtual is a singularity and represents singularization, this irreversible entering into indiscernibility of the virtual and actual as a process is called a crystalization.
The entirety of Cinema II can be seen as a refining and correcting in some senses of the Bergsonian insight into the distinction in duration between time's actual and it's virtual --and most important the appearance of distinct chronosigns that define uncharted territory for a given human subject.
The end point is to get the reader to see how they are created as subjects and see what ultimately what the ethological implications of the sign-types are (i.e. what does this all mean for you in terms of your next actions, perceptions, self-affections, or temporal contractions? etc).