An algorithm is a finite set of rules that gives a sequence of operations for solving a specific type of problem. Algorithms are widely used in calculating and computing. One good example of an algorithm is Euclid's algorithm. The concept of an algorithm is certainly not new, but the word "algorithm" is of rather recent vintage in English; Merriam-Webster's dictionary gives its first use as being in 1926.
The derivation of the word "algorithm" is curious. The word comes, via many intermediate stages, from Khowarizm, a town which is now the city of Khiva, Uzbekistan. One of the town's most famous residents is Al Khowarizmi, a ninth-century Arab/Persian algebraist, and his name became associated with "algorism," calculation with Arabic numerals, and from there the word gradually evolved into modern usage and spelling.