The wrapper is the last leaf a roller puts on. It has to stretch without tearing, lie smooth from foot to head, and still look like a single piece of cloth when the cigar is done. Factories pay more for wrapper than for almost any other leaf, because the defects show and because the leaf is in the smoke with every puff.
In Spanish the same leaf is the capa. Shade-grown leaves — Connecticut under cloth, some Ecuador under cloud — tend to be thinner and more elastic. Sun-grown habano and many maduro wrappers are thicker and oilier. Color names (claro, colorado, oscuro, candela) describe the finished look, not a separate plant.
A wrapper does not make the whole cigar. Filler and binder still do the bulk of the work. But a torn wrapper is a failed cigar, and a well-chosen one frames the blend so the rest of the leaf can speak.