What does Lacan mean by the imaginary order, symbolic order, and the Real? There's alot of equivocal writing about Lacan's 'three orders', but the best writing I know on the topic is Anthony Wilden's collection of essays in System and Structure. The basic idea is that the three orders relate to different ways of treating relations, that correspond in the following ways:
Real : Difference
Symbolic : Distinction
Imaginary : Opposition
That is, relations can be treated in terms of differences (real), distinctions (symbolic), or oppositions (imaginary). They are like different 'grades' of relations. Importantly, these grades of relation are hierarchically embedded, so that all imaginary relations are symbolic and real (i.e. all oppositional relations are distinctions and differences), and all symbolic relations are real (i.e. all distinctions are differences). As in:
Relations: {Real{Symbolic{Imaginary}}} ; Or:
Relations: {Differences{Distinctions{Oppositions}}}
The idea is that types of relations are characterized by a hierarchy of ascending generality, with differences at the top (the most general kind of relation), distinctions in the middle, and oppositions at the bottom (the least general kind of relation). If that makes sense, the next question concerns what characterizes each level of generality.
Starting from the 'bottom', imaginary relations, relations of opposition, are characterized by terms which are (mutually) exclusive (A ∨ B), and particular. By exclusive I mean that terms in this relation obey the logic of either/or: either A or B. To understand particularity, it's useful to contrast it with symbolic relations, which are relations of distinctions:
Symbolic relations are first of all not characterized by oppositional terms, but only distinctive ones. A father is distinct from a child, a chair is distinct from a desk. These terms do not oppose each other, and are not mutually exclusive (unlike imaginary relations). Furthermore, symbolic terms are not particular terms: a chair can be any chair, and does not refer to 'this' or 'that' concrete chair in the here and now. This is why the symbolic order is the order roughly correlated to language: in a language, we can make all sorts of distinctions that do not necessarily correspond to any particular thing or set of things.
The real is the hardest and most ephemeral to discuss so... I won't. Anyway, this is a very schematic way of treating the three orders, drawn roughly from Wilden's take on them. The psychoanalytic literature will tend to discuss these in other terms like desire, the Other, the mirror stage, the phallus, father-mother-child, and so on, which are all in fact appropriate and necessary to get the full sense of how these terms interlock, but this schematic rendering is hopefully helpful.
Wilden's work is hard to find, but two other works that I've found useful are Bruce Fink's The Lacanian Subject and Charles Shepherdson's Lacan and the Limits of Language. Zizek doesn't often do a good job explaining Lacanian concepts, imo. anyway, yeah, the abstraction and obscurity of the distinctions make them hard to explain, which is why there's so much waffle on them. Anyway, hope this helps.