In computational chemistry, the calculations which are performed involve very complex mathematics.
All data is the result of solving the equations describing the molecule.
The exact equations describing these molecules cannot be solved exactly, so approximations are created and then solved. These sets are a starting guess, or initial idea, about the molecule in question. Basis sets usually attempt to approximate the exact equations by adding up several other curves, called basis functions. The basis set chosen describes the number of basis functions used as well as the way they are added up. The name of a basis set is based on the number of basis functions used to represent different features of the molecule.