A fillet -- pronounced FIL-it, not like the cut of fish -- is a concept in engineering having to do with strengthening joints. It is mostly used in dealing with welding methods, but the concrete forms, such as in basements, are identical in principle, just not in material. The concept is simple: by adding more adhesive material -- such as concrete -- to a structural joint, that joint is made stronger.
The principle of any fillet is that in any area where two units, such as a wall and a floor, come together, the border area will be the first to break. If two boards come together to create a "T" shape, the expected stress will be mostly in that area where the two units come together. The fillet is used to alleviate this stress point. The point of the concrete fillet is to imitate, as much as possible, the concept that the wall and floor are the same structure. In some basements, the "monolithic" model of foundation does precisely this: concrete is poured into the entire foundation, creating a single unit where all walls and the floor are a single concrete unit. The fillet is used to imitate this monolithic structure.
Whether metal, glue or concrete, the fillet is based on the principle that increasing the surface area of adhesive relative to two units will, by that factor, increase its resistance. Concrete fillets are used usually in home or basement design and are not all that important in engineering. Commonly, fillets are used to strengthen the "joint" between the basement concrete wall and the concrete floor. This is the area of expected stress since it is a joint. One of the problems of any structural joint is that it is the weakest area of any structure. Hence, the concrete fillet might run the length of the floor and wall completely around the basement.
A fillet can be of different sizes. Using the basement example, if there has been real structural weakness between the floor and walls, possibly based on floor lifting due to a high water table, then the fillet is a first option. If the water table is pushing up on the floor, or alternatively, the floor is sinking down, there is then tremendous stress on the weakest part of the structure -- the joint connecting the floor and wall. A fillet can be applied that crates a triangle shape , a slanted "wall" that tightly connects and reinforces the wall and floor border.
The larger the fillet, the greater the strength. The idea is that the more of the wall and floor covered by the fillet, the strength of that joint will increase accordingly. In general, the fillet itself should be equally connected to the floor and the wall for maximum hold. Therefore, the variables in a concrete fillet are the amount of stress on the joint, the strength of the concrete compound itself and the amount of surface area covered on the wall and on the floor.