What are portals? "Doorways to knowledge." Wikipedia's coverage of subjects can be extensive (mathematics, for example, is covered by tens of thousands of articles on Wikipedia). Portals are an alternative entry to a subject (besides its main article), and to that subject's coverage in the encyclopedia, in a way similar to how the Main Page provides sample fare from Wikipedia as a whole.
Portals may include features such as Selected article sections, Selected image, news, points of interest (Did you know?, Anniversaries), and links to related Wikimedia. Portals are more diverse than the Main page, and may include features such as panoramic banners, slide shows, category trees, topics lists, and whatever else portal designers can come up with.
A secondary purpose of portals is to provide bridges between reading and editing, and between the encyclopedia and the Wikipedia community. They may provide links to the related WikiProjects, Wikipedia's Reference desk, and so on. Portals are a hybrid between encyclopedia pages and project pages, and occupy their own special namespace, the Portal namespace. Therefore, all portal titles are preceded by the prefix "Portal:"
The list of all completed portals is Portal:Contents/Portals. A list of all portals, including those under construction, can be found at Category:All portals. The Portals WikiProject is dedicated to collaboratively building and maintaining portals, and further expanding on the Portal concept, such as with automated features, and is always looking for new participants.