The main source is, of course, the OSM database itself. From the planet.osm dump many different statistics are calculated and entered into taginfo.
The wiki contains description of keys and tags and much more. Currently taginfo will collect all the Key:xxx, Tag:xxx, and Relation:xxx pages (and their different language variants) and extract the information from them (not just those tags listed on Map Features).
Taginfo gets some information from style rules in JOSM. THIS WILL BE REMOVED SOON. JOSM support has been rolled into the 'Projects' source, see below.
Taginfo gets information about the different languages of the world, their codes, names, etc. from several IANA and Unicode registries.