Context - as I understand the term - means that some information can not be interpreted alone, but needs additional information to make sense. A simple example is personal communication where: "Bill has married" makes only sense when both sides have a clear preference what "Bill" means. Sozial sciences use context in a broader way to include all our cultural and religion inheritage which we use implicitely in all we do.
In the wiki this means that the pure wiki page information "title + text" is not enough to predict what we will see on screen. There is at least a template for the layout of the page, a "wiki dialect" that's implied in the software that interpets the markups. There is general wiki configuration data and user preferences. All this determines how the webpage created from the page data looks like. Not only that, it also may influence what links and functions are available and what we can to with the page.
Typically this isn't too complicated because the context is the same for all pages in a wiki. At least that's what we are used to. But this needn't be the case. Live becomes very interesting when we give a degree of freedom to the context of wiki pages. We need this for WikiFractality, because we must be able to change at least some page properties. But the context offers much more than that. But it tends to become mind-boggling.
There are lots of different types of contexts:
It's incredible that all these (and even more context types) can be useful for wiki applications. The only real problem is how to cope with the complexities. I think its important to do this "problem driven" and offer only those features to the users that really help for their problems. Otherwise the overall effect is negative. It's hard enough to grok a simple wiki.