For use in annotating the work of an Italian poet, I wish to explain a reference to An sich and für sich: What would be a brief, straightforward, and yet accurate definition of these concepts in Hegel's philosophy?
Sebastian Gardner compiled a Hegel glosssary which is extremely useful if one is looking for concise definitions as a starter. I doubt that you will find many definitions to match your criteria better than these.
That being said: Easy definitions of Hegel's concepts are kind of a self-contradictory idea, so if there are still some question marks above your head, it may be due to Hegel being Hegel (some years of extensive studies help, he's actually quite on spot as soon as you understand the system).
FOR ITSELF (für sich). Reflective, explicit, self-comprehending, fully developed (Miller often translates für sich as 'explicit'). Contrasts with: in itself, in-and-for-itself.
In a sense, the for itself is the subject relying completely on the inner sense, on observing and contemplating upon the stream of consciousness and its own ideas and thoughts. The input from anything out of the self is completely commensurated and assimilated so that there is nothing "alien" and everything that there is is explicit. In a way, the pure self-relation of a subject. In Hegel's later systematic works, it is closely related to the terms representation/perception or the concrete/particular.
IN ITSELF (an sich). Merely potential or implicit (Miller often translates an sich as 'implicit'). Something is 'in itself' when it is considered separately from other things, and (in the case of a form of consciousness) when it is unreflective. That is why, for Hegel, the in itself is mere potentiality: actuality requires determination, negation, relations with other things. Note that a thing may be 'in itself for us' (an sich für uns), an expression Hegel uses often: this just means that we are considering it as it is separate from other things. Contrasts with: for itself, and in-and-for-itself.
The in-itself is an object (including the self if observed as a mere object) considered as everything that it is (or rather: can be) if we look only at it and not all the relations through which we conceive it. That is why it is also a consideration of something as pure potentiality, ie. this is an abstraction. In Hegel's later systematic works, this is closely related to the terms concept or the abstract.
A related concept which should be kept in mind is the synthesis of both of them, the in-and-for-itself:
IN AND FOR ITSELF (an und für sich). Completely developed; both at home with itself, and finding itself in the other. It contrasts with mere being in itself and being for itself. Being in-and-for-itself is the condition of the Absolute, God, Spirit actualised.
Here, the self realises that the in-itself that it considered as alien from it was actually alienated from itself by itself, ie. it recognises itself in that which it considered as being separate from it. Hegel is adamant that the potentiality of the in-itself can only exist as actual when being assimilated into (considered as actually taking place in) a for-itself and, in turn, the pure actuality of the for-itself is nothing and can only exist if it solicits itself in the form of actualised potentialities.
In other words, in-itself and for-itself are illusions and at the same time necessary states or steps in a process of cognition where in the end, the self realises that it is an actualisation or an instance of "potentiality actualised" of the Weltgeist. This ideal of knowledge coming to itself is closely linked to the term idea or the reality in Hegel's later works.