What is an Algorithm?
In its most general sense, an algorithm is any set of detailed instructions which results in a predictable end-state from a known beginning. Algorithms are only as good as the instructions given, however, and the result will be incorrect if the algorithm is not properly defined.
Examples of Algorithms
A common example of an algorithm would be instructions for assembling a model airplane. Given the starting set of a number of marked pieces, one can follow the instructions given to result in a predictable end-state: the completed airplane. Misprints in the instructions, or a failure to properly follow a step, will result in a faulty end product.
A computer program is another pervasive example. Every computer program is simply a series of instructions, which may vary in complexity, and is listed in a specific order, designed to perform a specific task. Mathematics also uses algorithms to solve equations by hand, without the use of a calculator. One last example is the human brain: most conceptions of the human brain define all behavior — from the acquisition of food to falling in love — as the result of a complex algorithm.
http://www.wisegeek.org/what-is-an-algorithm.htm