It seems that we all have privileged access to our own inner sensations. I am directly aware of my pain, but everyone else can only surmise it or be told about it. However, it is difficult to talk coherently about the nature of this privileged access. "I know I am in pain," says no more than, "I am in pain." Saying that sensations are private is not a statement of fact so much as a grammatical statement about how we are to use the word, "sensation."
Wittgenstein confronts the difficulties of talking about inner sensations with the idea of a private language: if it is possible to talk meaningfully about my own sensations as something that only I have access to, then I should be able to formulate a private language that refers to these sensations so that no one but myself will understand it. Suppose I take note of a certain sensation, and write "S" in my diary on every day that I experience that sensation.
The practices that surround our ordinary language-games and give them meaning are absent with private language. There are no criteria for saying whether I have understood or am using "S" correctly, and so "S" has no clear function. There is no distinction between what is a correct use of "S" and what seems correct to me. Without an external means of justification, there is no concept of justifying the proper use of that sign.
One of the peculiarities about privacy is that we have no access to other people's private experience: your sensation of red may be totally different from mine. When we talk about "red," we are not talking about our own private sensations, but a common experience of what we call "red." Though we can talk about sensations such as color-impressions or pain, we only talk about them insofar as they are common experiences.
This is not to say that there is no such thing as pain, but only pain-behavior, or that sensations only exist insofar as other people can share them. Rather, it is meant to highlight what "pain" means by observing how we use the word. "Pain" does not simply refer to an inner thing in the same way as "chair" refers to an outer thing: it is accompanied by a whole set of notions about what it means to be a person who feels, senses, lives, and so on. We do not learn how to use "pain" from our own experience of it, but from our shared experience, from observing other people having similar experiences and talking about them in similar ways.
Suppose everyone has a box with something in it, but people can only see the contents of their own box and nobody else's: different people may or may not have different things in their boxes. We could call this something a "beetle," but the word "beetle" does not play the role of a name in this language-game: what is actually in the box is irrelevant to how "beetle" is used. Private sensations are not objects that we refer to, because referring to them becomes irrelevant if only we experience them.