Why does this game end in a stalemate?

Forgive my ignorance, but I'm trying to understand something...  While playing against the computer, I've had several games end in a stalemate, when I seem to be within one move of checkmate.  Here's one such game, where I am white.  Upon moving Qa3, the game ends stalemate, and the assistant tells me Qb4 would have been best (which would have forced black to Ka1 or Ka2, which I could have followed with Ra3 to win).  But with my Qa3, black would have put himself in check with any of the five possible moves, so I'm not sure why it ended in a draw.

Is this a rule that I am not aware of?  What is the rule?

Your queen (a3) isn't covering black's king (b1) square, but all surrounding squares are covered.

Thanks @GaryHopple, but I'm still confused.  I understand that I have Qa3 did not check black (b1), but I don't understand why this is stalemate.  Black must move, and any move will result in a loss. 

I guess the rule is that I can't force the opponent into a position such that they are forced to move into a position of checkmate?  I suppose it is just strange to me that this results in a draw.

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