Merriam Webster dictionary defines recursion as “a computer programming technique involving the use of a procedure, subroutine, function, or algorithm that calls itself one or more times until a specified condition is met at which time the rest of each repetition is processed from the last one called to the first.” Recursion by definition is the technique to call itself to generating the elements of a domain generated by special condition. It is used in different areas of studies and has numerous significance.
In computer science programming recursion is used to compute, analyze, manipulate, and construct databases. For instance, recursion is used in sorting and searching algorithms such a binary search for a binary tree. Recursion is a bit different that than iteration. It is more efficient in terms of run time complexity. People say that there are some costs associated with using recursion as it is copied onto the stack each time it calls itself, and this takes time & memory which is actually not required for solutions. To the contrary, the use of recursion makes the computer be able to keep track of what event happened in which part of calculation/function.
Recursion is not only used by machines but it has other significance on our daily life. One might get amazed when one comes to know that the Fibonacci sequence which can be generated by recursion can help in approximation of Kilometers and conversion to miles and vice versa. [For details here] By the way, Fibonacci series can be computed by other method than recursion. Use of recursion for this series actually makes it complicated. Nevertheless, there is one function called Ackermann Function which cannot be used without iteration. Ackermann function uses different condition for different domain and it can be used as a benchmark of a compiler's ability to optimize recursion This shows the actual importance of recursion in mathematics and daily life. This is one application for recursion, and there are whole bunch of them which can take whole life to discuss.