Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.