In Philosophical Investigations (1.293) Wittgenstein introduces a famous and memorable analogy: the beetle in the box. Suppose everyone has a box that only they can see into. No one can see into anyone else's box. Each describes what he or she sees in the box as a 'beetle'. I know what a beetle is from my own examination of what is in my box, you from yours. Wittgenstein points out that in this situation while we all talk about our beetles, there might be different things in everyone's boxes, or perhaps nothing at all in some of them. The thing in the box, could be changing all the time. Whatever it is, he maintains that it cannot have a part in the 'language-game'. Analogously (and this is only implied rather than fully spelt out by Wittgenstein), if I say that I know what 'pain' means from personal introspection, on the model of what he calls 'object and designation' - like the ostensive definition (or, as non-philosophers put it, pointing) that tells us 'that's a cat' when I point at the furry animal in the garden - then whatever 'internal' object Im pointing at (the equivalent of the cat) drops out of consideration. It is irrelevant to the meaning of 'pain'. It is like the beetle that may or may not be in the box.
This is part of Wittgenstein's so-called Private Language Argument (of which there are numerous competing interpretations). The gist of this is that the assumption that introspection governs the meaning of our sensation language is false: language is rule-governed public behaviour (though, perhaps perversely, Wittgenstein denied that he was a logical behaviourist, though some of his interpreters find this disengenuous). Language is far more enmeshed with the world and our forms of life than those who (perhaps influenced by Descartes and his legacy) see the mind as essentially a private theatre would have us believe...
This post relates to the course Philosophy in the Gallery at Tate Modern.
These links are useful for an overview of Wittgenstein's life and philosophy:
Numerous further links at episteme.com