Arming the door means activating the escape slide so that it will open in the event of an emergency. Disarming the door means deactivating it. F/A's arm the door, visually cross check the f/a's door across the aisle from them and then say over the PA "1L 1R, 2L 2R" etc. to verify that the door has been armed/disarmed and cross checked. It is the hope that all of these visual and verbal checks will decrease the number of slide deployments.
On some airplanes certain doors remain armed at all times, such as on the A330...3L and 3R remain armed all the time. One of the exits on the 757 also stays armed, but I can't remember exactly which one it is right now.
There is also a panel in the cockpit of the Airbus fleet that shows if the doors are armed or disarmed, and on the A330 there is a screen on the f/a panel showing this as well.
Even with all of these precautions in place f/a's still manage to inadvertantly deploy the slides from time to time, and the cleaners and ground people have been known to blow a few too. Not a good thing, very expensive and it usually puts the airplane out of commission for a while.
Hope that answers your question.