A deckle edge on a sheet of watercolor paper is an uneven or frayed edge. It's the natural edge that is formed when paper is made, where the paper pulp thins out at the edges.
A full sheet of handmade paper usually has deckle edges on all four sides. A sheet that has been cut will have one or more straight edges, depending on how it was cut. Some machine-made papers have simulated or 'artificial' deckle edges.
The photo above shows the deckle edge on a sheet of Fabriano watercolor paper. It's been held up to the light so you can see how the paper thins in the deckle edge (and the watermark).
The width of a deckle edge varies from manufacturer to manufacturer. On some papers it is quite narrow; on others it is quite wide and intended as a decorative edge to the sheet. Some artists like to keep a deckle edge and to frame a watercolor painting so it shows; others trim it off. It's a matter of personal preference.
