Generally speaking, an internet meme is a variation of a theme that occurs over and over again throughout the blogosphere. An example on a grand scale is the Hitler getting pissed off video, which has been reconfigured for things as disparate as Michael Jackson's death, the problems with the iPhone 4 antenna, and Vuvuzelas at the World Cup.
In the mommyblogosphere, a meme can also be another way of referring to a carnival, or a weekly (or other regular, repeating) thematic scheduled event hosted by a blogger. The blogger will host the event on their blog and invite other bloggers to post according to the same theme on their blogs and link back to the original blog, and receive a link in return. Often badges for the meme or carnival are created as well. This is a way of building traffic and community in the mommyblogosphere, not to mention clutter in sidebars.
See also: carnival