Cigarillos seldom use a binder. But for larger cigars, they can allow you to roll more solid cigars, and to use a thinner, more fragile wrapper.
Binders should have few holes, and be sturdy enough to tightly wrap the bulk of filler. Binders need to have at least a moderate combustibility. You can combine a potent binder with a mild wrapper to alter the taste and aroma.
Wrappers just need to be relatively intact. They can be thin or thick. The heavier the binder, the thinner the wrapper can be. A truly durable wrapper, like the Besuki sold at WLT, can often be used without an underlying binder, though the resulting cigars are seldom as well compressed as those that also use a binder.
A binder can also be useful when rolling a cigar (even a large cigar) of entirely shredded filler. The binder is used to just loosely hold all the shreds in a rough cigar shape. When the wrapper is then applied, it's the wrapper that contains all the compressive force--an easy task with shred.
Bob