He comes to feet means that, due to good positioning play, he (i.e. the attacker, Alexis) manages to move himself into relative positions where the midfielders (e.g. Wilshere) can kick the ball cleanly and directly to him on the ground.
Spins in behind means after he gets the ball he quickly gets goal-side of the defender.
I think it's clearer in this quote, coincidentally also about Arsenal:
“Walcott is 26 and if Wenger’s going to stick to what he’s been saying, he has to give Walcott a run as that centre-forward.
“I think he offers a bit more than Giroud going in behind defences, he stretches defences and defenders hate running back towards their own goal.
“From a midfielder’s point of view, if you’ve got a willing runner to get in behind and threaten defenders, it gives them a different option rather than Giroud who comes to feet all the time.”