When you play basket ball you flick/push your hand out very quickly to grab the ball.

To flick means to move something out very quickly. It's not a very common word. It's most often use to either (a) quickly throw something (he flicked the ball to another player) or (b) something like a frog's tongue. (the frog flicks his tongue out and catches a fly). in this case it means the defensive guard's hand moved away from his body very very quickly toward the ball. 'flicking' also has a connotation of lightness, not being very heavy. (i.e. the movement is not very strong, just very fast)