The term was coined in The Selfish Gene and only discussed during the chapter on universal Darwinism. The concept was to make a comparison between human mimicry and cellular evolution. Both have a replicating piece of information that changes over time and competes for finite resources. In memetics, the finite resource is the human mind, the replicator is a gesture, mannerism, saying, etc.
Memetics is very new so it’s still in a state of flux. Different researches differ in how they define it and how broad it should be. At its most limited, using the original argument above, it must be devoid of usefulness to a human. Ideas related to survival aren’t memetic. The best example to explain this is language; the form of a language is memetic, the content is not.
The opposite end of the spectrum is a definition of memetics that includes all ideas. In effect it’s any part of the human brain’s software which isn’t hard wired. All things taught to new humans are memetic then. I like this definition but I can also see the critiques of it. It’s already a soft science that’s very hard to study. It may be better called a philosophy of culture than a science. It’s still in it’s infancy so I won’t rule one as more or less valid than the other. There will be legitimate and important scientific conclusions from it’s continued study.
I will tend to use the latter definition because I find it most useful for what I’m interested in studying, that being culture and humanity.
Lastly, a memeplex is a term I use when discussing more complex things. Memes themselves are individual ideas, kernels of culture if you will. A memeplex is a collection of those taken as a single entity. Think of a biological ecosystem but for memes.