This is a link to the state of the article as I found it. Before touching it I threatened to improve it, but no-one responded, so I've made it better. If you prefer you can look at the diff.
Ironically, perhaps, the dictionary definition was most helpful in resolving the problem. So the answer is threefold:
1. Any formal system of reasoning that arrives at a truth by the exchange of logical arguments.
Or, put another way, hardly to be distinguished from discussion, except we emphasise rationality and put aside appeals to emotion (and we'll quietly forget that many of the actual Socratic dialogues don't do this). This I think is part of my annoyance with the philosophers: adding a word that can only just be distinguished from a commonplace word, so as to make their sentences more high falutin'; and then failing to distinguish different meanings of their shiny new word carefully.
2. A contradiction of ideas that serves as the determining factor in their interaction.
This is the Hegelian version. Subtly, the concept of evolution or process has come in; in that things start in one state and end in another. Quite exactly what it means is up for grabs; if you believe Popper it allows contrary ideas to stand and is thus the death of reason; if you're an Hegel fanboi it will mean something subtly different; as you can tell I'm not a great fan of big H. But that's OK; my purpose on wiki was mostly to distinguish things.
3. A progress of conflict, especially class conflict.
This is the Marxist version. TBH I'm still not entirely sure what it is, but I think it just takes the "process" idea and runs with it; the connection with the original meaning has become rather tenuous at this point.
There's another point - which I'm not fully sure of - which is that dialectic doesn't fit well with formal logic. The arguments can all be logical, of course, but it relies on a process of evolution, whereas logic is timeless. Anyone able to explicate that more clearly - or refute it - is welcome to try.
And there you have it. If you have any interest, or even philosophical training, I encourage you to improve the wiki article too. As long as you agree with me, of course.
* Jesus and Mo.