Cheezburger’s Know Your Meme answers this best:

An Internet meme is a piece of content or an idea that's passed from person to person, changing and evolving along the way.

A piece of content that is passed from person to person, but does not evolve or change during the transmission process is considered viral content (different from a meme).

Internet memes have risen in popularity with the rise of Internet Culture as more and more people identify with and participate on the Web as their primary method of expression and content consumption.

Cheezburger’s Know Your Meme is dedicated to documenting Internet phenomena: viral videos, image macros, catchphrases, web celebs and more.

For example a LOLcat (pronounced "lull-cat") is a meme because people attach different human behaviors and funny captions to images of cats. Click the meme below to view all the memes made from this image. 

Meme by: macdonaldc