"Looking-Glass" is the Victorian name for a mirror – since, you know, it's a piece of glass (with a foil back) that you use to look at yourself. Mirror images are reflections – reproductions, with a difference, of the real world. They're the opposite, or the backwards version, of normal things, and throughout Through the Looking-Glass Lewis Carroll will play with different kinds of reversal, reflection, and opposition. Sometimes it's time that seems to work backwards, such as when the White Queen bleeds first and then pricks her finger. Sometimes it's distance, as when Alice has to walk toward Looking-Glass House in order to get away from it. Sometimes cause and effect are themselves reversed, such as when Alice and the Red Queen have to run in order to stand still.
What's most important to notice about these different forms of reflection and reproduction is that they're not consistent. Carroll introduces each of them for a moment or scene, but they're just throwaway jokes. Alice doesn't have to run to stand still for the entire book, for example. This tells us that we're reading satire and parody, which make the most of a pun or a conceit and then let it drop, rather than science fiction, in which we'd have to worry about the consistency of the rules of this new backwards world.