The title says it all. I am just interested to explore the objections briefly. I'll really appreciate if all is explained in layman's term and suggestion to helpful material is also welcome.
The term picture theory of meaning refers to Wittgenstein’s description of language in his book Tractatus logico-philosophicus. From its 7 main propositions number 4 and its sub-propositions deal with language.
Proposition 4: “The thought is the significant proposition. (= Der Gedanke ist der sinnvolle Satz.)”
Proposition 4.1: “The proposition is a picture of reality. The proposition is a model of the reality as we think it is. (= Der Satz ist ein Bild der Wirklichkeit. Der Satz ist ein Modell der Wirklichkeit, so wie wir sie uns denken.)“
Different interpretations for „picture“ have been suggested. One interpretation takes “picture” as mapping in a mathematical sense. Accordingly, a picture is a structure preserving mapping from the proposition to reality, i.e. the structure of the proposition resembles the structure of reality. This covers the property of a “model” to represent the structure of the domain of investigation.
Already this Ansatz of the picture theory can be questioned from the viewpoint of constructivism: We do not know the structure of reality, hence we cannot determine whether the proposition maps to its structure. All we can do, is constructing from our sensory input due to repeated experience a model with its structure. As Kant puts it: The thing in itself is not recognizable. Wittgenstein presupposes that reality has a structure which resembles the logical structure of our propositions. Notably, he presupposes a logical structure of reality resembling the logical structure of purged language.
In my opinion, such view overestimates the role of logic as the primordial structure of reality. Overestimation, because reality exists much longer and previous to information processing according to the rules of logic.
In Wittgenstein's own development, he moves on from the picture theory to an interpretation in terms of 'games' which capture actions and motives.
(I like the "Blue and Brown Books" which are notes from his lectures during the period this change was taking root. Since he was speaking to humans, it is more comprehensible than the "Tractatus", and holds together more tightly than the "Investigations")
Actions can in some sense be captured by a sort of 'moving picture', but not in a way that reliably feels like a basic concept has been really captured. We do not so much accumulate these moving pictures, as look behind them for shared structure and how that structure answers to motives. If I teach a child about an activity, at some point fairly early on, unless the motivation is really obvious, she moves on to 'why' before being willing to put up with any more 'what' or 'how'.
And internal wishes and motives are not as easily captured in pictures. If a person did not have the direct experience of hunger, you would not be able to depict it, only its effects, so you would have extreme difficulty conveying the actual 'picture'. But by demonstrating the effects, you are only pointing at the motivation to avoid them, and not very clearly. For less physical motives like power or love, things get worse and worse.
But the fact we share motives shapes what we do, and those actions coalesce into negotiations around the motives, even when we do not explicitly discern and point at the motives. Carousing, for instance, serves a genuine need that we generally do not bother to name. But it creates a grand and sprawling vocabulary and a set of rules for negotiation and optimization of the experience. (Ask any autistic or any other earnest-enough introvert how stupid these really seem on their surface, or maybe just anyone from a distinctly different generation.)
Most other kinds of objects have importance to us to the degree they are parts of schemas that answer to motives. When they do not, we can point at them, but the reference is unlikely to become a stable part of our shared language. Non-farmers do not tend to have multiple of different words for dirt, even though we can and do probably occasionally point at varieties of dirt when they matter to us, whereas farmers do. In the picture theory of language, both people should find the relevant pictures equally cogent and memorable.
That indicates that the much more ambiguous category of social motives is what matters to us. (A statement so obvious it is almost a pun.) And we do not pursue any basic approach to just describing reality, including exchanging pictures.