In mathematics and computer science, dynamic programming is a methodology of the solution of the problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The methodology takes much less time rather than naive methods.
The term was originally used during the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programmer, which restates an optimization problem in recursive form.
The word "programming" in "dynamic programming" has no particular connection to computer programming in general , and instead of this it comes from the term "mathematical programming", a synonym for optimization. Therefore, the "program" is the optimal plan for action that is produced. For example, a finalized schedule of events at an exhibition is sometimes called a program. 
Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem. For instance, 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. After this, it is using this to pick the best overall path. In a word, we can solve a problem with optimal substructure using a three-step process.