The ferrule is the piece of metal that holds the bristles to the handle of a paintbrush. The size, material, and design of the ferrule matter more than you might think!
Stainless steel or nickle plated ferrules are better than ones made from other materials, because they do not rust as much. This is most important with watercolor brushes, as rust on the inside will eventually stain your images. It matters for other brushes as well, because a good brush, treated properly, will last 10, 20, or more years.
The ratio of the length of the bristle inside the ferrule to the amount of bristle outside the ferrule is also important - it affects how firm the bristles are. Brushes with most of the bristle outside the ferrule with be floppier, whereas brushes with more bristle inside the ferrule are more firm. The brushes with the least exposed bristle, brights, are very firm.
It is important to be sure, when painting, to never never never let the paint get down to the ferrules. This is not so important on the outside of the bristles, but moreso on the interior bristles, because it is just about impossible to get the paint out of there. Once the paint dries in there, that effectively becomes the anchoring point of the bristles, and the advantage of having a long ferrule is lost.