A watermark is watercolor paper's equivalent to the sewn-in label in a piece of clothing -- it tells you who made it. Depending on the manufacturer, it may also tell you more, such as the brand and the cotton content.
The watermark in the photo above, for example, tells you not only that this sheet of paper is manufactured by Fabriano, but that it's a sheet of Artistico. (Fabriano is said to be the first company to use watermarks, starting towards the end of the 13th century.)
Watermarks are most easily seen by holding a sheet of watercolor paper up to the light. A watermark can be added either by it being part of the screen used for making the paper (it shows up because less paper pulp is used in this area), or by it being embossed (indented) onto the paper when it is still wet.
Incidentally, holding a sheet of watercolor paper so the watermark reads correctly, doesn't mean you've the "right" side of the paper facing towards you. How it's done differs between manufacturers. Neither is the absence of a watermark a sign that it's a cheap 'n nasty piece of watercolor paper.
