If I am in pain and someone is tuning a piano, I can mean two different things by the words, "it'll soon stop." But in what way do I mean, or direct my attention toward, the pain or the piano tuner? Do I somehow inwardly point to one or the other? No answer seems to suggest itself, and yet I cannot doubt (nor can I know) what I meant when I spoke. To mean something is not to think of something. The surrounding context, and not a mental state, provides the criteria for what is meant.
The last 300 sections of Part I deal with various questions in the philosophy of mind, jumping about in a much less directed way than the discussion of understanding in sections 38–184 or of rule following in sections 185–242. Many of the remarks here date from an earlier stage of Wittgenstein's thinking, and many of them connect in various ways to some of the more focused discussions earlier in the book. This is not to say that these sections lack value, but that, partly by virtue of the nature of the investigation itself, it is difficult to identify any particular direction or conclusion that we can draw from them.
Wittgenstein's main preoccupation is to analyze our tendency to think that words like "believe," "recognize," "wish," "mean," "hope," and so on correspond to particular mental states. One reason for thinking like this is that we can say words without meaning them, and we can say we believe something without believing it. As a result, we feel that there must be something more than just the words that constitutes the meaning, believing and so on. Because there is no tangible "something more" that we can identify, we associate it with an intangible act of the mind. Wittgenstein tries to show us that there is no mental "something more" that we can plausibly expect to do the job we want it to.
Of course, the matter is not this simple, and Wittgenstein approaches the problem from many angles to tease out what is wrong with many of our preconceptions about the mind. Precisely because a great deal of the Investigations—as well as a great deal of the rest of Wittgenstein's later writings—deal with these very problems, we can infer that Wittgenstein takes them to be very difficult.
His method is not to give us answers to the questions we raise about the mind, but to try to make these questions dissolve altogether. He wants to show us that questions of how we can believe things, mean things, and expect things, do not expose difficult mental problems that we somehow pass over when believing, meaning, or expecting in our everyday lives. We are creating puzzles for ourselves that are contained not in the act of believing, meaning, etc., but in the forms of expression that we use to talk about these acts. Thus, the investigation deals largely with grammatical questions in the hopes that a proper understanding of this grammar will show us how we come to conceive of these problems as problems. His aim is stated explicitly in section 464: "to teach you to pass from a piece of disguised nonsense to something that is patent nonsense." The questions we ask about the mind cannot be answered because they are nonsensical, but we do not recognize this. His investigations aim to bring this fact to light.
The conclusion, if there is one, is that we have to become more conscious of asking the wrong kinds of questions. An exemplary case is Wittgenstein's treatment of "guessing the time," in section 607. I can genuinely guess the time, or I can say the exact same words with the exact same expression but while reading off a script or practicing elocution. The absence of outward criteria by which we can distinguish genuine cases of guessing from these other cases leads us to suppose there must be some inward criteria. We then ask what sort of a mental state or process "guessing the time" could be. Wittgenstein's answer here is similar to his remark about the meaning of "slab" as "bring me a slab" in ¤20. We can only talk about a certain case of saying, "what time is it?" as being "genuine" because we can contrast it with cases of reading off a paper, and so on. That is, we would never have thought to ask if there were some special feeling accompanying the utterance of the words "what time is it?" if no alternative interpretations came to mind.