I am asked this question quite frequently and thought I'd explain to the best of my ability from an educational perspective.
Websites sit in the web 1.0 category and are the original format that information was shared across the web. A website has a limited number of authors and were in large content based. The viewpoints of the authors were the only perspective available and besides email or submitting a form, interaction was very limited with the audience. Ownership and Audience interaction are the two key disadvantages of web 1.0.
Web 2.0 is very different in the fact that it has the ability to be highly interactive with the audience and can build communities of like-minded people. Wikis combine the features of adding 'static content' or information as well as developing collaborative content within a community. (Wikipedia is a good example of this)
The aim in education when using wikis is to build students knowledge and capability in co-constructing their learning. Because wikis are editable, students have the opportunity to use web 2.0 tools to demonstrate their learning with the input of others collectively. They become the authors and in so doing their learning becomes transparent.
I would certainly encourage teachers to use wikis to gather resources, display learning outcomes etc for student reference, but the idea is to use wikis to include scaffolding so students become more independant and then interdependant learners. This is certainly the intent of the nz curriculum vision of enabling students to be 'confident, connected 21st century learners'.
Community: If we are co-constructing learning with our students we need also to define the role of the teacher. Wikis provide us with the opportunity to involve parents, other classrooms and teachers. With effective use the input we can have on a child's learning stretches far beyond the walls of the traditional classroom. The students become teachers and the teachers become facilitators.