The most popular wiki platform is
Mediawiki, the same software used, among others, by Wikipedia. It's written in PHP, so if you've already hosted PHP apps before you'll feel right at home. If not, there's a
comprehensive documentation on how to install and configure it.
It has a ton of configuration option so you can tweak it to suit your needs, but at the same time offers pretty sane defaults so you can get started using it right away. On top of that, there are hundreds of
extensions provided by the community in case you need changes not available in the base app.