The central insight of the later Wittgenstein can be stated simply, though its implications are vast: meaning is use.
A word does not mean what it does because it pictures a fact, or because it refers to an object, or because it corresponds to a mental image. It means what it does because of how it is used in practice, in the context of human activities and social life. Meaning is not a thing attached to a word. It is a pattern of use embedded in a form of life.
Wittgenstein introduces the concept of language games to make this vivid. A language game is any rule-governed use of language embedded in a practical activity: the builder and his assistant who use a vocabulary of "slab," "pillar," "beam" as part of their work. The child learning to identify colors by pointing. The priest performing a ritual. The scientist reporting an observation. The person comforting a grieving friend. Each of these is a language game: a form of linguistic activity with its own rules, purposes, and criteria for doing it correctly.
The point of the language game concept is not to trivialize language by calling it a game. It is to emphasize that language is always embedded in activity, in practice, in forms of life that give it its point. You cannot understand what a word means by staring at it in isolation and asking what it pictures. You understand it by seeing how it is used: in what contexts it appears, what people do with it, what counts as using it correctly, what difference its use makes to human life.
This leads to Wittgenstein's critique of philosophy. Most philosophical problems, he argues, arise from language going on holiday: from taking words out of their normal contexts of use and asking questions about them in a void. Take the word "know." In ordinary use, it works perfectly well: "I know where the keys are," "Do you know how to drive?" These uses have clear criteria, clear contexts, clear points. But then the philosopher asks: "Can you ever really know anything?" "How do you know the external world exists?" "How do you know other people have minds?" These questions take the word "know" out of its normal context of use and ask it to do philosophical work it was never designed for. The result is not profound insight but a kind of bewitchment by language: the appearance of a deep problem that is actually a grammatical illusion.
Wittgenstein's goal is not to answer traditional philosophical questions but to dissolve them: to show that they rest on misunderstandings of how language actually works, so that once you see the misunderstanding clearly, the sense of a problem evaporates. "The philosopher treats a question like an illness," he writes. Philosophy is therapy, not discovery.
The concept of forms of life (Lebensformen) is one of Wittgenstein's richest and most discussed contributions. A form of life is the broader human background that gives language games their point: the shared practices, habits, reactions, and ways of being in the world that make linguistic activity possible and intelligible. Language does not get its meaning from a private inner realm of meanings and intentions. It gets its meaning from its embedding in a shared form of life. This is why a radically alien form of life would be literally incomprehensible: "If a lion could speak, we could not understand him." A lion's form of life is too different from ours for its language (if it had one) to be intelligible to us, even if we could somehow translate the sounds.