Every faction has one such spy (each with his own flavor). The reason they exist is purely one: card advantage.
lets say that you won round 1.
you want to exhaust cards from your opponent on round 2, so you play your spy. You draw one card (so basically you didn't lose a card) and FORCE your opponent to play one of his own cards (because if he passes you can 2-0 him)
another way to play spies is to slow down tempo.
let's say you are 20 points ahead of your opponent. You are afraid he has some high tempo play, or you dint want him to win with just 2 cards, on the flipside, if you play a normal card, let's say a 10, bringing the difference to 30, he'll SURELY pass, making you "waste" your 10 power card.
in such a case, you play your spy, you're still ahead, and you effectively didn't spend a card.
lastly, it was much more important in the previous patch, but there are some times you need to go last no matter what, I.e. you have a 20 str unit on hand and you know opponent has a scorch, Card Advantage give you exactly that, by "drawing a card" you effectively one up your opponent on who has the last play