What might be the earliest-known entry of the word "algorithm" in a dictionary can be found in Samuel Johnson's Dictionary of the English Language from 1785.
The entry on page 130 reads (approximately):
algorithm: Arabic words, which are used to imply the six operations of arithmetic, or the science of numbers.
Today, "algorithm" is defined as:
- A well-defined procedure to solve a problem.
- A clearly specified set of simple instructions to be followed to solve a problem.
- A finite, deterministic, and effective problem-solving method.
- An explicit, precise, unambiguous, mechanically-executable sequence of elementary
- A sequence of computational steps that transform input into output.2
1. Jeff Erickson's algorithms notes
2. Introduction to Algorithms / Cormen, Leiserson, Rivest, Stein / MIT Press link
See also: wikipedia