A recursive algorithm is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem. It typically involves a function that calls itself with modified arguments until it reaches a base case, which is a simple instance that can be solved directly. This approach is often used in tasks like calculating factorials or traversing data structures like trees. One key aspect of recursive algorithms is their ability to break complex problems into simpler subproblems. This can lead to elegant and concise code, but it may also result in higher memory usage due to multiple function calls. Understanding recursion is essential for computer science concepts, including data structures and algorithm design.