The binder is the leaf that holds the cigar together. After the bunch has been formed, by entubado, an accordion fold, or another method, the binder is wrapped around it so the filler stays in place on the rolling table and in the mold. In Spanish this leaf is often called capote.
The binder has to burn well. A binder that does not burn properly can make a cigar burn unevenly on one side (canoe), burn down the center (tunnel), or go out. It also has to be strong enough to hold the bunch without adding much flavor of its own, although some binders are chosen because they do add flavor. A double binder uses two binder leaves, either because one is not enough or because the blender wants a particular burn or taste.
You rarely see the binder on a finished cigar, because its job is structural rather than visual. See wrapper and filler for the other two leaves in a typical cigar.