In chess, player with the white pieces has been traditionally considered having a slight advantage in virtue of the right to move first. How significative is this advantage has been debated for an eternity, but it is generally agreed that if there is a player with the advantage in the starting position this can only be White.
The right to move is a great thing because it brings us close to achieve our plan (assuming that we are playing good moves!). Indeed, imagine for a second that you could froze your opponent for 5 moves in the starting position. Logically, you would be granted a great advantage because you will be able to develop your pieces while he achieves nothing.
There exist, however, a set of situations where you would prefer not to move if you could, as making a move could only worsen your position. This concept takes the name of zugzwang. Germans have a word for everything :)
Consider the position below, where each king is defending his own pawn and attacking the opponent's pawn. Would you chose to play it with Black or White? The answer depends on who has the move! In fact, whoever moves first loses, as the king will be forced to abandon the best square of the position (as the king is already sitting there!), losing the pawn.
Another example that I really like it's a study position.
Angos, 2005
The endgame king and 2 knights vs king is a draw. However, in this particular situation White wins with 1.Ne6! Nd8 (Black would really like to sacrifice his knight, but White is not going to accept it), 2.Nf6+ Kh8 and now 3.Ng5 (diagram). Without the black knight this would have been a draw for stalemate. Instead, with a knight on the board the stalemate is not an option. Black cannot stop checkmate next, for instance 3...Nf7 4.Nxf7#
I hope you understood that having the right to move is not always an advantage!
And may the zugzwang be with you.
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