Recursion: base case vs. small version
When you use recursion to solve a problem, you typically partition your input into one or more smaller instances (and possibly a part that you don't process further). Those smaller instances are what your exercise calls the small version.

Upon recursing, your inputs get smaller and smaller until it is no longer possible (or sensible) to further split them up. The inputs that are left to be solved directly are called the base case.