The cap is the small piece of wrapper that closes the head end of a cigar, the end you put in your mouth. After the wrapper is rolled around the binder and filler, the roller seals the head with one or more small pieces of wrapper leaf glued in place with a vegetable-based adhesive (gum tragacanth, traditionally). The cap holds the rolled wrapper in place and prevents it from unravelling.
The cap matters because cutting it correctly is the difference between a clean draw and a cigar that falls apart. A proper cut takes off about an eighth of an inch from the very top of the head, sitting just above the cap line where the wrapper finishes wrapping the body. This opens the cigar enough for smoke to flow without removing so much that the underlying wrapper can unwind.
Cutting too deep into the cap is the most common rookie error in cigar smoking. Once the cap is gone, the wrapper has nothing holding it together at the head end, and it begins to unravel as you smoke. Within ten minutes the cigar may visibly come apart in your fingers.
Cuban cigars traditionally use a triple cap (three small pieces of wrapper layered at the head), which is a marker of traditional craftsmanship. Many modern non-Cuban cigars use a single or double cap; both function equivalently when properly applied.
For more on cigar construction, see The Anatomy of a Cigar.