In computer science and mathematics, an algorithm is a set of specific instructions that, when executed, lead to producing an output. The computation proceeds through a finite number of successive states until it terminates in an ending state (output).
A cooking recipe is one real life example of an algorithm. Ingredients (input) are successively added and processed (computation) in a pre-defined time frame, which results in a particular dish (output). Several different recipes may result in a similar dish.
Algorithms are commonly used for data processing purposes, calculation, and automated reasoning. The constantly updated Google search algorithm is just one example Check out this Gizmodo blog post to understand more about ‘the algorithm that rules the Web’.
You can also check out the Algorithm problems for dummies blog for some more easy-to-digest examples. And here is another blog about algorithms. Interested in creating algorithms yourself? Check out this top coder tutorial site for some valuable resources on the subject.