An algorithm is a set of steps for solving a problem. I'm pretty sure the usage has been around for about 7 or 8 decades at least. I'm not sure that it's actually applied to PC's, per se, but to the programs that run on them. The advent of the PC almost certainly had the effect of widening the use of the term, as did the subsequent rise of the net.

Knuth's "The Art of Computer Programming", the first book of which is entitled "Fundamental Algorithms" was started in 1962 according to wiki, but it the concept was developed even long before that by church and Turing:
http://en.wikipedia.org/wiki/Algorithm

In practice, I seldom see the words routine and algorithm used interchangeably. Usually a routine refers to a piece of code, while an algorithm refers to "pseudocode", or to a verbal description of a process, or sometimes to just a set of equations or a mathematical formulation. (That's not *really* the correct use of the term algorithm either, but that's the way people use it.)

Other similar words are "procedure", "subroutine", "module" (often a collection of related routines), program, code (as "a code"), "method", "function", "subprogram" - again, though, none of these are exactly the same. In some sense you might be able to use the term lay term "process", except that word is already laden with meaning in CS.