When a reusable mylar stencil is created, bridges (sections of mylar that hold the centers of letters (such as a,b,d,e,o,p,q) together are cut out. These stencil bridges are what support the stencil and give it the form. I like to refer to them as the "support section" because without them your stencil would be floppy and unusable.
The big advantage to using a stencil with bridges is that it's well, reusable. If you don't like how the bridges look once your done stenciling you can paint over them.