Leading edge is a line connecting the forward-most points of wing's profiles. In other words, it's the front edge of the wing.
It may be equipped in one or more of the following:
The air advancing towards the wing, first meets the leadnig edge. Therefore, in high speed aircraft (such as Space Shuttle), it can cause extreme heating of this surface. This was the cause of the accident of Space Shuttle Columbia during re-entry on February 1, 2003. The accident was caused by a small damage to RCC tiles on the leading edge, which occured during take-off.