They tack, which is the name for a particular type of sailing maneuver.

You might think — because this is what's most obvious — that a sailboat works by unfurling its sails, pointing in the direction in which the wind is blowing, and then making headway because the wind pushes it forward. This turns out not to be the case, though. Sails are actually much more subtle and interesting than that. The way a sail works is by acting like a wing and generating lift. As the wind passes over the sail, the sail generates lift which propels the boat forward, but not in the direction the wind is blowing. Depending on how the sails are rigged, the boat makes headway at an angle to the wind.

As a statement of general principle, a sailboat can make headway at up to a 45° angle to the wind. That means if the wind is blowing from the north (that is, toward the south) then a sailboat can sail in any direction from northwest all the way around to northeast, including east, south and west. This Wikipedia picture shows what I mean.

So in general, as long as there is some wind, a sailboat can probably sail toward its destination. The only time it can't is when the intended destination is right smack into the wind. When that happens, the sailor tacks into the wind, sailing a zig-zag course. In that previous example I said the wind is out of the north; if the sailor wants to sail north, he'll first sail northwest for a while, then change tack and sail northeast for a while (or vice versa; doesn't matter). In this way, the sailor can make headway into the wind, even though it takes a while.