To "get into" something means to become interested in it. For example, if you recently started reading books about history, you can say:
I've been getting into history lately.
If you think that someone will like a video game that you're recommending for them, you can say:
I think you'll get into it.
You can also say that you "are into" something, which means that it's an interest or hobby of yours:
I've always been into martial arts.