I'm speaking about Aikido. I'm 5. kyu, and I don't have any experience on other martial arts.
When the uke is in balance, it's hard to move him. Atemi is a strike to do this. Atemi doesn't have to be a real painful punch, although it can be. One of the favorite atemis of mine is a real punch that any person who is awake will try to dodge. The idea is to move the fist determinedly directly towards the uke's face, when he isn't prepared for it. A reflex will make the uke to move backwards, disturbing the balance. The punch doesn't have to hit. When I'm the uke, I find it impossible to prevent this reflex from working. One variation of this is snapping fingers instead of a fist. That is so unexpected that you get 1.5 seconds extra time when the uke ponders what's happened.
I have heard of some funny atemis. Cleavage for a woman is very effective to disturb the male. It works even for many senseis. Remember that all you need is one little glance, one small crack in the stone of concentration and WHAM! Men have also another weakness: when doing iriminage, you need the uke to bend his body forwards. Men will voluntarily bend their body forwards if you threaten their crotch. Yet another atemi is knuckle-rubbing the sternum. It is actually used as a test for unconsciousness. Accidentally inserting fingers to the mouth or nose when doing tenchinage will make anyone fall down. Kids, don't try this at home.
Anectodes from http://www.aikidofaq.com/