It's best explained using examples:
Let's say there are 9 players at the table and the action begins:
- UTG raises
- UTG + 1 and UTG + 2 both call
- UTG + 3 makes a 3-bet
- Hijack, Cut-Off, Button and the blinds all fold
- UTG, UTG + 1 and UTG + 2 all call the 3-bet
So now, the players in the pot are: UTG, UTG + 1, UTG + 2 and UTG + 3.
Because UTG + 3 was the last aggressor in that round (he made the 3-bet, the others just called), it means that he has the lead in the next round. This does not violate the order in which the players act, they still act in the same order (first player left of the dealer).
OK, now we go to the next round of betting:
Usually, what you would see in such situations is that UTG, UTG + 1 and UTG + 2 all check to the guy in the UTG + 3 position (the one who has the lead). If, at this moment, he bets, then it's said that he made a continuation bet, sometimes abbreviated as c-bet.
However, sometimes this does not happen: if the UTG checks, but the guy in the UTG + 1 bets (a.k.a. BEFORE the UTG + 3 guy has the chance to act), then it is said that the guy in the UTG + 1 seat leads out. This means that, by betting, he takes away the lead from the UTG + 3 guy.