A "meme" is a unit of cultural information. As with many ideas there are several different interpretations of exactly what a meme is, but my personal interpretation goes like this:
My understanding of the idea of the meme is based on my understanding of what constitutes "life".
"Life" consists of a pattern of information that is so structured that it tends to replicate (make copies of itself) and in doing so sometimes changes (mutates). Usually when the pattern changes it does so in a way that makes it less likely that the pattern will succeed in replicating, however sometimes a particular change will occur that is "beneficial" to the pattern, that is, the altered pattern is more likely to replicate than the unaltered pattern.
Philosophers who thought about this definition of life noticed that this behaviour was not only limited to matter, but was also displayed in other media. An example of another medium in which patterns of information replicate is the medium of information that is stored in a computer system.
Computer viruses are so-called because they exhibit similar characteristics to biological viruses. They are essentially patterns of information that tend to create copies of themselves, and spread through all of the available region.
Another medium in which information is altered (or processed) and travels around is the human mind. The human mind processes enormous amounts of information, in the form of music, the written word, symbols, spoken langauge, images, noises etc.
As I understand it, a "meme" is the smallest unit of this sort of information. This is where it becomes difficult to give the word a precise definition. If we are to take the meme in its purest sense, as an elaboration of an analogy taken from the world of biology, then a meme is equivalent to a gene. A gene is a unit of genetic information, and a meme is a unit of "cultural" information.
There is a problem with this. A "gene" is a discrete unit of data encoded as a series of chemicals. No one seems very clear as to whether a meme is the label for some as-yet-undiscovered unit of human experience ("experions" ;-)) or is a label for a "mind virus", which it is often used as.
"I can't get "The 5th of Beethoven" by the Electric Light Orchestra out of my head!" said Bert.
"That's because you have caught a meme!" replied Alec. "A meme is like a computer virus, but for someone's brain."
Another similar problem is with the definition of "culture". Stating what is culture and what isn't is controversial at the best of times. Comparing memes to genes means we have to compare culture to biology (now I come to think of it - what is biology exactly?).
So to summarise: a "meme" is a self-propagating unit of cultural information that may take the form of an idea, concept, song, phrase, habit, mood or something else. No one has decided exactly what a meme is. However I suspect that a fairly good example of a meme is the idea of the meme itself. By writing this I am reinforcing the meme, and I am helping it spread.
As with genetics, there are some memes that are beneficial (using the word in the woolly sense of part gene/part mind-virus) and there are others that are not. Religions comprise a collection of memes that are generally quite successful in the sense that memes of certain religions are very common in several cultures and often form a central part of the culture.
An example of this is morality. Morality is the ideology of the Christian religion, and has taken a central role in the traditions of Western democratic, progressive, liberal cultures like that which is the main culture in the UK or France.
However, as with genetics, the driving force of memes is their own self-propagation. A meme doesn't necessarily have to benefit the people it uses as its "vector", it only has to ensure that the individuals it infects/occupies/uses survive long enough to spread the meme to several other people, and that the individuals spread it as effectively as possible.
As always, all the self-referential cork screw thinking involved in thinking about memes leaves me quite tired. There are many questions surrounding the somewhat ambiguous concept of the meme, and no one seems very sure as to what the answers might be.
Anyway, if you want to read a clearer description of the meme and what a meme is I suggest you go to www.en.wikipedia.org/wiki/Meme