Wow, that is a big question. It might be best to Google "present continuous" and find some grammar sights to to explain that in detail.
I would just say, that in my opinion, the most frequent use of the present continuous is to talk about the future plans. In fact, when expressing future events, the present continuous is probably the most frequently used way of doing so - at least in spoken English.
e.g. - What are you doing this evening?
- I'm staying home; there's a good movie on TV tonight.