What features does DirectX have?

it is difficult to give a precise answer in a couple of words: the directx libraries are huge. However, the idea is that these libraries expose an api (a set of instructions) that allow game programmers to easily develop software. For example they don't have to deal with the particular aspects of each video card: that is done by directX and by the drivers.

What kind of functionality directX expose: for ex. you have an image and you need to move it. Passing appropriate parameters, directX will do that for you. Also there are implementations for sound, etc.

This is what one can do with directX. It is the bread and butter for game programmers that target Microsoft platforms. Make no mistake though: you don't get to do something till you spend some time studying.