A meme is an an idea that is remembered and passed on, and in competition with other ideas is remembered and passed on more often.
An internet meme, e.g., the University of California policeman attacking students with his can of pepper spray, transposed into famous works of art, is not a meme: it is a running joke. But not only that.
This idea or image is being passed on, but it is not any quality of that idea itself that gets it remembered and makes people want to reproduce it. It is commentary on the idea that performs these functions. We remember the commentary, and are driven to comment ourselves, reproducing or adapting the commentary. The original image does not provide the meaning.
In fact the internet meme is often actually making the point that the subject is without meaning: a University Of California policeman "protecting public health and safety" pepper spraying students sitting down at a campus square, or, to take another example, an actor famous for his ridiculous roles as a man of strength.
The idea that is remembered, and gets itself reproduced, is the making of a community of commentary.
Cooperation between individuals rewards each individual when they live together: when everyone likes to give, and finds it's even better to give to people who have greater need, giving works. In such a community of everyone giving everyone gets too. Recent re-evaluation of the biology of altruism is coming around to this, living together dependent, conclusion. (See this recent New Yorker article, and this 1975 article.) Altruism is not the product of ideas, nor of genetics, but of both, actions, ideas, and chance too, creating the right circumstances.
Internet memes are models of action, in action. They create communities in which altruism works. An idea, in both examples it happens to be mockery of well known figures, create communities where altruistic acts, the creativity of each joke maker, reward each other.
It is incorrect to see this process as a competition between ideas to get themselves remembered and reproduced. If there is a meme here at work, it is the idea of community formation itself being passed on, not through words or images, but within the entire community's actions.
Ideas in the social world that do act like genes as units of evolution commonly are repressive and ritualistic rather than creative, and tend also to be false: nationalism. racism. free-market economics*, etc. What are known as internet memes are something different and better than that.
Ideas that compete to be remembered and passed on, that act like memes, destroy the ability of people to question the common elements, the reproduced elements, of social life. But ideas that compete to make a community of commentary increase the ability of people to understand and help each other. And, to repeat, hopefully in a creative way, what is reproduced is not any particular idea, but the favorable circumstance creating model itself of making life better.
* G. Q. Chesterton pointed out a century ago about the free market "meme" that it was idiocy to suppose something good could come from a mechanism of everyone being bad.