Different prepositions have different meanings, so you can approach this by learning the basic meanings of these three prepositions, and then try to apply those basic meanings to this specific context. However, this is not the right approach to take. If you want to learn the meaning and use of any word, whether it's a preposition or a concrete noun, you should study example sentences that illustrate the meaning as well as possible.
But having said that, and with that very firmly in mind, I'll give a brief explanation:
1. He's changed in the last two years.
The time phrase in the last two years expresses a period of time starting two years ago and leading up to the present time. At some point between the beginning and end of the period, there was a change. The preposition in means 'occurring at a point in time that is located between two other points in time', i.e., the endpoints of the period. What's important to understand is that the change is viewed simply as a single event.
2. He's changed over the last two years.
This is similar but it adds meaning. The time phrase over the last two years expresses a similar period. The preposition over means 'occurring from one endpoint to the other endpoint of the period'. In other words, the change is viewed not as a single event but as a gradual process.
3. He's changed within the last two years.
It's harder to imagine someone saying this. The preposition within is very similar to in in that they both mean 'occurring at a point in time that is located between two other points in time'. What gives within an extra meaning is the emphasis on these limits. In this case, it's like saying sentence 1 but with an added message of: 'Please do not misunderstand me—I want to be clear that the change took place at some point in this period.' You'd have to be a little creative to come up with a context to show someone having a reason to make such an emphasis (though of course, with enough imagination you can).
As I said at the beginning of the post, if you want to understand the meaning of within, you should work with more readily illustrative examples.