The binder is the leaf wrapped around the filler tobaccos to hold the cigar together. It sits between the wrapper (the outer leaf, the one you see) and the filler (the inner blend of leaves that produces most of the smoke). A finished cigar has three components: filler at the centre, binder around it, wrapper around that.
Binders are not chosen for their visual appeal because no one ever sees them. They are chosen for their structural and combustion properties. A good binder holds the filler in place without crushing it, burns evenly with the wrapper at the same rate, and produces clean smoke that does not interfere with the wrapper’s flavour. A poorly chosen binder can cause uneven burns, tunnel-shaped ashes, or harshness that tracks back to combustion problems rather than the leaf itself.
That said, binders do contribute to the flavour of the cigar. They are leaves of similar character to the wrapper and filler, often grown in the same region, and they add their own subtle notes to the overall profile. A Mexican San Andrés binder, for example, lends a dark cocoa note that supports a maduro wrapper; a Nicaraguan binder lends pepper and earth that pair well with full-bodied filler.
For more on cigar construction, see The Anatomy of a Cigar.