Full disclosure here is that I'm very much an interested amateur at this point - there are people who have spent many years thinking deeply about memes and memetics, and I'm not one of them. But the basic concept is kind of beautiful and not very hard to grasp, and it does give us some insights into how science works.
We should start with some definitions. A meme is a unit of information (such as an idea or concept) that's copied from person to person. The idea of memetics is that memes are subject to an evolutionary process because they are copied, a range of variants exist, and they are subject to selection pressures (some memes spread more effectively than others). So what we then have is a way of thinking about the dynamics of how (scientific) ideas evolve and develop.
It strikes me that science in particular is a memetic process where we have one additional concept: we subject our memes to the selection pressure that they must be confirmed empirically. This is an important difference. Memetics per se does not require any given meme to be true; it just has to be good at propagating. This explains why rumours that are false but appealing can spread so readily. By adding the additional constraint of empirical confirmation, we are adapting memetics in order to learn about the universe.
Thinking in this way, we can define a list of general scientific processes in which we can be involved.
- Validating an existing meme or memeplex (empirically or via theoretical proof or computational analysis)
- Improving an existing meme or memeplex (someone had a good idea, then you're able to refine it)
- Making a new memeplex (a new combination of memes)
- Creating a new meme
There may well also be others that this interested amateur hasn't yet thought of :-)
One additional thought is that this also gives us some insight as to how important is it to fill your brain full of relevant memes, so that you've got more to work with.