An open-ended wrench with one jaw fixed and the other adjustable by means of a screw positioned at the point where the working end of the wrench starts to flare out from the handle. Although this wrench is indeed shaped like a crescent, its name actually comes from the original manufacturer, Crescent Tool Company, which began production in upstate New York in the early 1900's.
The company's founder and the wrench's so-called inventor, Karl Peterson, really did nothing more than buy the design from a Swedish immigrant, who had seen similar wrenches made in his homeland. Nevertheless, Peterson was soon filing lawsuits against anyone else who dared make an adjustable wrench, as he held the patent for it. Nowadays anyone can make them legally, but those with the "Crescent" name tend to cost much more, presumably for reasons of prestige.
Enough of the depressing history - the tool's function is far more important. Its extraordinary usefulness comes from its ability to turn nuts and bolts of a variety of sizes, made to specifications of any measurement system. Regular wrenches can only handle hardware of a specific size, and so come in sets of either standard (the old English units, still commonly used in the United States) or metric sizes. A crescent wrench can be adjusted to the size needed for any particular nut, either standard or metric. (This is the basis for a common joke played on apprentice mechanics, who are asked to find a "metric crescent wrench"). It's always a good idea to take one along when traveling by automobile or bicycle.