What are algorithms?

I particularly like the Economist's "explains" section, where they unpack words/phenomenon that experts in the field take for granted in terms that a layman can understand.

This is their take on algorithms:

> An algorithm is, essentially, a brainless way of doing clever things. It is a set of precise steps that need no great mental effort to follow but which, if obeyed exactly and mechanically, will lead to some desirable outcome.