How is this scenario a draw? Firstly, I'm very very bad at chess. I've known how to play for most of my life, but I've never been good, so I'm trying to get good by playing against easy computers.

I commonly end in draws with situations like the following:

3k4/8/1N6/2P2Q2/4R3/R5B1/P3K1P1/5B2 w - - 0 1


I'm really not convinced this is a real draw. I have both Rooks and my Queen left, so I should be able to box the King in easily. But maybe I'm wrong, maybe it's impossible for me to win.

So if I'm wrong, I'd like to know why. If not, why does the computer consider this a draw?
With black to move, he is not in check but he also has no legal moves. There is no square where his king can go without putting himself in check, and that would be an illegal move.

That situation is called stalemate (Wikipedia), and it is an immediate draw by the rules of the game. You've boxed him in too well.

As to why stalemate is a draw see Why is stalemate a draw? , and there are also a lot of further questions if you search the site for "stalemate".