Draw??

Hi. I'm new to chess, and it's addictive.  While playing the computer, I've has several matches come up as draws, like this one:

I'm white. How is this a draw??? It looks like I won. Thanks for your time 

this is called stalemate. It is really annoying and happens when you move your pieces and black can't move anywhere while they're not in check. search it up/.

To avoid stalemate, be sure that opponent either has a legal move or is checked by you. (Side note: at the position you present, Qa3# would win instead.)

P.s. might be unrelated, but you can analyze your games once they're finished, allowing you to see your mistakes (with explanations if using premium report). This might help understanding some simple things and blunder less.

Always make sure the opponent King has a square to move to on his move unless your move is checkmate. If the King can't move and he's not in checkmate, it's a draw.

Queen to a3, or Rook to a8 would have won you the game.

Its called stalemate, your opponent has no legal moves to play so it ends in a draw. I recommend you search up en passant as well as it might get tricky if u encounter it.

What is the point in butting in days later and repeating what a dozen guys have already said?

Yeah. It happens when the king can't go anywhere but it is not check

Why couldn't the queen take the rook in that case? This is what's confusing me.

The black King on a7 cannot take the Queen on a3.

You must mean the King, not the Queen. The black King wouldn't be able to take the Rook on a8 because the Rook would be defended by the Bishop on d5.

Others have already explained: it is a stalemate. According the rules of chess it is a draw: https://en.wikipedia.org/wiki/Stalemate

Do some Mate-in-1 puzzles about Checkmates - once you learn the difference between Checkmate and Stalemate you will remember it for the rest of your life There will be a Lesson or two on this site about it.

Basically the opponent's King doesn't have any squares to move to in either case, but in Checkmate it is under direct attack and will be captured if there was another move, but in Stalemate he escapes and can never be captured because he isn't directly under attack but has no legal moves So ask "If White had one more move, could the Black King be captured?" If not, it is Stalemate and a draw.

And the Rook on a8 would be defended by the Bishop (the King can't capture a defended piece because it would mean the King can be captured on the next move = Game Over!).

It sounds complicated but you will get the hang of it all after a few days doing Mate in 1 puzzles.

Practicing on the Analysis board (or in the Practice Drills section) against computer simple King and Queen vs King checkmates will help you understand how to avoid stalemate too. Watch a YouTube video and practice this!

When new players first encounter stalemate, it is usually in this kind of instance - one player is so dominating the position that it is impossible to understand why the other player should be awarded a draw.
The thing is, the stalemate rule covers a variety of situations and simplifies the rules (rather than have 2-3 different rules for what happens in a stalemate-type situation. 
Stalemate can happen, as here, where player A is dominating and player B has no available move. It can also happen in situations where player A has the extra material but stalemates themself (usually, these are composed positions, but it is possible).
But where stalemate really comes into play most of the time at the higher levels is in subtle situations where one player has only a slight advantage, but the other player has stalemate tricks to help them try to save the game. One example is the K+P vs K endgame. Without stalemate, the K+P will always win. With stalemate, you have to know what you are doing to win with the K+P. Another example is where you may be one move away from being checkmated, but you have a rook that you can use to check the opposing king by moving right next to it and where taking the rook would leave a stalemate.

Thank you, everyone! I'll check out the training videos.