A viral meme occurs when a concept or idea is integrated into a group of people to the extent that the concept or idea spreads like a virus "infecting" each individual as it goes before incidentally spreading usually by word of mouth to other individuals.
A prime example of a viral meme is the All your base are belong to us
which spread around the internet
for a few months and like many popular memes' spawned
variants and mutations
of the source
How exactly a viral meme is propagated is of great interest to both those that study memetics, psychologists and marketing people for being able to understand why one thing is considered cool and why another thing is not can form the basis of many papers and strange adverts.
A good analogy of a viral meme is that of a fire generally a meme will burn out quite quickly lasting at most a few days before a better meme is found however sometimes whilst the meme is not as popular it will continue to be propagated for a long time.
In the case of all your base are belong to us the meme was not only very popular but it also continued to be propagated by various methods for quite a long time.
A viral meme never really dies it simply fades into obscurity awaiting to be re-discovered at some later date.