The end point of this is that we can construct or describe language with language. I wish I had another term for this concept because it's a tad intimidating/pretentious, but I can't think of one. It has to do with two particular features of language that we use pretty well constantly.
The first is the ability to create terms that refer to chunks of other concepts grouped together. Douglas Hofstadter makes a very big deal of this in his lecture on Analogy as the Core of Cognition. We build concepts then group them to create a new concept that consists of, at least, all the chunk's constituent concepts. I say at least because there is a gestalt that operates almost invariably when we do this concept chunking thing. I define reflexivity without mentioning chunking, but that's ok: chunking is referential in nature, but just operates on groups.
The second feature of language we use is its inherent capability to use it to discuss or describe language itself. This hardly seems like a feature because we do it all the time when we teach and learn about language, but we create language to serve our mental capacities, one of which is to reflect on the important things we do, such as use langguage. Natural languages are not perfectly suited to this (languages we speak and write versus contrived linguistic constructs such as computer programming languages), as evidenced by our reliance on phonetic gizmos when we write about how to pronounce a word, but it works well enough.