Most games that involve taking turns, with one player going first by lot or agreement, have some sort of advantage to going first. Tic-tac-toe, for instance, is a guaranteed draw for player 1, assuming correct play. Connect 4 is a guaranteed win for player 1, assuming correct play. The first move in Go is considered so powerful that player 2 receives a bonus of 5.5-7.5 points. The first-move advantage in Chess is less obvious, although statistically speaking White has an advantage of ~52-56%.
White's advantage is essentially that of time. He can count on starting ahead of Black and in theory should not go behind except by choice. He can even attempt to trade material for time.
Black's advantage is that of choice, or response. She can let White develop the game as he chooses, or she can force the game into a different line of play altogether. Presumably she knows her purpose in playing her responses to White, and can take advantage of White's loss of choice.
This being said, does it have meaning outside the highest levels of play? Is the game theoretically close enough that there isn't a way to equalize it 100%? (Related previous discussion suggests that the first move is "worth 25-45 rating points". However, the question didn't directly deal with the first-move advantage, instead referring to it tangentially in a discussion of handicaps.)