A wiki is a type of website that anyone can edit, with Wikipedia being the most popular example. Anyone can run their own wiki and use it however they’d like for whatever purpose they desire. They’re incredibly useful for collaborating with audiences large and small, and don’t need to be long term websites. How you use a wiki is completely up to you.
As a student, I’ve made wikis for specific group projects for collaborating outside of class. Unlike phone calls or email, information was preserved and available for the entire group to see. We could update them whenever we wanted, from wherever we wanted. We could build on each other’s work, make changes a little at a time, and even search. Once the projects were done, their wikis were simply deleted. Throwaway wikis can be very useful.
There is an overwhelming number of wiki solutions to choose from. You might be tempted to choose based on number of features, but a wiki is a collaborative tool. It should be simple and easy to use. PBworks is free, takes about a minute to set up, is hosted for you, and will be extremely easy for the other people to use. If you want a self-hosted wiki and your server supports PHP, I recommend PmWiki. If you don’t have PHP, WikiMatrix is a comparison site that may help you decide.
MediaWiki is noteworthy for powering Wikipedia and having many features, but in my opinion there are easier-to-use options available.