In mathematics and computer science, dynamic programming is a method of solving problems, that exhibit the properties of overlapping subproblems and optimal substructure. The method takes much less time than naive methods.
The term was originally used in the 1940s to describe the process of solving problems where one needs to find the best decisions one after another. 
The field was founded as a systems analysis and engineering topic that is recognized by the IEEE
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. Thus, 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, an algorithm.
Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem. For example, the shortest path to a goal from a vertex in a graph can be found by first computing the shortest path to the goal from all adjacent vertices, and then using this to pick the best overall path.
In general, we can solve a problem with optimal substructure using a three-step process:
1.Break the problem into smaller subproblems.
2.solve these problems optimally using this three-step process recursively.
3.Use these optimal solutions to construct an optimal solution for the original problem.
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.