Note for others who view the other answer: what's pictured is quarter-round moulding, not base shoe.
Base Shoe moulding (also referred to as Shoe Base or simply Shoe moulding) is quarter-round's tall, thin cousin. It's typically 1-1/2 to 2 times as tall as it is wide, and it's specifically intended to cover the vertical gap between the floor and the bottom of the baseboard. (Google "shoe base" to see an example.)
Quarter-round is a quarter segment of circle, and equal dimensions in its height and width. It's often installed as shown above, to hide the expansion gap required by wood flooring. Some people would call this a half-azzed installation and you will not find fat quarter-round used in high-end installations. A more aesthetically pleasing (but more time consuming) solution is to remove the baseboards, and use the baseboards to hide the expansion gap.
Because of shoe moulding's relatively small size, it is fairly flexible and it's often possible to simply bend it to follow the floor. Scribing and planing are effective to address high spots, but if you have a large dip in the floor and you scribe both ends of the run to accommodate the low spot, you then have a problem at each each corner of that wall, where the moulding must mate up with its neighbor on the adjoining wall.