To most people, a fillet is a piece of meat. The word takes on other definitions when it comes to woodworking and architecture, and it can refer to several specific parts of a molding or turned piece. In these instances, the word is pronounced "fill-it," not "fill-ay," but that's only the start of the confusion. The exact meaning of the word must be gathered from its context.
The most basic definition of a woodworking fillet is simply a rounded edge. Picture a square piece of wood -- if you were to cut a corner straight across to remove the 90-degree angle, it would be a chamfer. But if you made a radius cut, resulting in a smooth, rounded transition between the two adjoining sides, the corner would be a fillet. The term also applies to edges -- if you were to use a fillet router bit along the edge of that piece of wood, the edge would have a smooth, rounded transition from front to back, much like a bullnose edge on a counter top.
Sometimes, the word fillet refers to the way two pieces of wood are joined. Picture a wooden box -- when the wood is initially joined, all the corners where perpendicular pieces of wood meet are 90-degree angles. If you were to fill the corners with epoxy or putty and smooth it to produce a rounded transition between adjoining surfaces, that would be a fillet joint. It's the same profile as the fillet cut but with a concave, rather than convex, curve.
The fillet profile doesn't always refer to a rounded edge. In architectural and some furniture design, a fillet refers to a skinny, protruding profile with a vertical edge, even if there are 90-degree angles. Picture a column -- the raised areas between the depressions in the flutes are called fillets. In crown molding, a narrow band that sticks out further than the rest of the molding's profile -- like a picture rail -- is called a fillet. Fillets can also be "sunken," meaning a depressed, rather than protruding, area.
In wooden staircase design, a fillet is an actual piece of molding, not a profile. In fact, the profile of the fillet piece is flat and straight although the edges may have a very small radius fillet curve. These pieces are used to fill the spaces between the balusters that hold up the handrail. Although not structurally essential, they help ensure even baluster spacing during installation and provide a more finished look to a completed staircase.