A meme is "an idea, behavior, or style that spreads from person to person within a culture."
A meme acts as a unit for carrying cultural ideas, symbols, or practices that can be transmitted from one mind to another through writing, language, gestures, rituals, or other imitable phenomena.
A macro image style internet meme. image: R.Conan-Davies/imgur
The term was coined by Richard Dawkins in his book 'The Selfish Gene"published in 1976. A meme is considered a unit of human cultural evolution analogous to genes.
Memes now most commonly associated with a style of internet image (macro image) and overlaid text, often a variation of quote from a popular movie.
Reference:
http://en.wikipedia.org/wiki/Meme
See also
Know your Meme for useful background and history of memes