Where does the word meme come from?

In the The Selfish Gene (1976) the scientist Richard Dawkin expands the Darwinist concept natural selection to the realm of ideas.

Just as genes propagate themselves in the gene pool by leaping from body to body via sperms or eggs, so memes propagate themselves in the meme pool by leaping from brain to brain.

This usage of meme has seeped into general English. Here on BBC Radio 4's Start the Week discuss the idea of  a 'cultural meme':

What is an internet meme?

The term internet meme strays some distance from the Dawkins' definition. It describes something that quickly becomes popular online. Examples of internet memes include the Harlem Shake and the phrase FAIL.

fail – v., n., adj.a youthful expression to summarise a bad situation or experience.

Most internet memes are ephemeral and quickly pass into obscurity. A few have endured - Rickrolling from 2007, for example. This suggests an online natural selection, of sorts.