Traditionally it's a social gathering where people tell stories, sing songs, play music and maybe dance. It has morphed a bit into more of an actual dance, especially in the south of Scotland, but in either case the dances are Scottish country dances, often danced all "wrong" according to the book but with verve and enthusiasm. These latter events are more properly described as "ceilidh dances".
(See the Tips and Notes for the "Family 2" skill.)
Mostly it's the footwork that is the difference. There are some dances that are more frequent at ceilidhs but the formations aren't that different, but nobody cares if you get your steps right as they do with the actual Scottish Country Dancing (well even there there are some people I just don't look at their feet)