Delete game trash can symbol

I notice this on a few games, Is it the opponent asking you to delete a game or is it saying they deleted the game or want to.

I also notice that a few players resign once I take their queen or start doing good..that fact that I'm not really 'good' makes me laugh when that happens..I've won 2 games from same person who resign!
hahaha

The trash can on your 'my games' page means that either you or your opponent can delete the game. Once black completes their second move, the option to delete is no longer available and you have to play out the game.

You'll be able to see how good you are as compared to the guy you beat twice once you've played 5 games, and that "rating" is more solidified as you play more.