Base shoes complete the look with both aesthetic value and function. They cover up the angle at which the baseboard meets the floor, creating a smoother look overall. Since they jut out from the wall, they also defend the baseboard from impacts or scratches from objects like vacuum cleaners, which move about on the floor.
Shoe molding is much the same as quarter round having the same 90° angle on the backside but instead of being a perfect quarter radius its profile is a bit more squat. The main use for shoe molding is to run along the intersection of the baseboard and floor.
Using shoe molding gives the floor installer more latitude in their end cuts and also allows the trim carpenter to hide un-level floors. Since the shoe molding is such a small and flexible piece of trim it can meander up and down with the floor hiding the unevenness with much less work than with just a baseboard.