A watch crown is the small knob on the side of the case, usually at the 3 o'clock position, that you use to set the time and date. On a mechanical watch, it also winds the mainspring that powers the watch.
What the crown does
Pull the crown out and turn it to set the time; many watches have an intermediate position for the date. Push it all the way in for normal wear. On a hand-wound or automatic watch, turning the crown while it's pushed in winds the mainspring. The crown is your main point of contact with the movement, so it does several jobs depending on how far you pull it out.
Crown positions
Most crowns have two or three positions. Fully in is the resting and winding position. The first click out is usually date-setting. The next click out is time-setting, which on a hacking movement stops the seconds hand. Learn the positions on your own watch and you'll set it correctly without forcing anything.
Crowns and water resistance
The crown is essentially a hole in the case, so it's a weak point for water. Better watches seal it with gaskets, and dive watches add a screw-down crown that threads shut against the case. Always make sure the crown is fully pushed in — and screwed down if it screws — before the watch gets near water.