Dynamic programming is a method used in mathematics and computer science to solve complex problems by breaking them down into simpler subproblems. It involves storing the solutions to subproblems in a table or cache, allowing for efficient computation of larger problems by combining the solutions of these smaller subproblems. Dynamic programming is particularly useful for problems that can be broken down into overlapping subproblems, where the efficiency of the solution can be improved by storing and reusing intermediate results. It is commonly used in algorithms for optimization and decision-making problems, such as the shortest path problem, the knapsack problem, and sequence alignment in bioinformatics.