I know you checked Wikipedia - not sure what link - here is a good overview:
http://en.wikipedia.org/wiki/Computer_form_factor
Cases will support specific motherboard form factors. So case specs will tell you what motherboard form factor(s) it will support. Many cases will support multiple form factors.
The three most common for PCs are:
ATX - Traditional full size motherboard with full expansion capability. Used mostly in Full Towers, Mid-Towers, ATX Desktops, and Large HTPC cases. Typically 4 or more expansion slots and 4 memory slots plus all the bells and whistles.
Micro ATX - Smaller variant of ATX. Used mostly in mid- and mini-towers, slim-sized desktops, and smaller HTPC cases. 2-4 memory slots, 2-4 expansion slots, not as much room for features.
ITX (or mini-ITX) - Smallest of the 3. Used specifically in ITX enclosures. Used for mini PCs, small form-factor HTPCs, and compact gaming rigs. 2 memory slots, typically only 1 expansion slot.
Cheapest is typically Micro-ATX. ATX is more because of more features. ITX is more because of trying to fit everything on a smaller board.
These are also backwards compatible, so an ATX case will typically support all 3 (though it would be sort of silly to put an ITX motherboard into a full tower)
That's about it. There are other form factors, but those are by far the most popular. As you get experience, you'll come to understand the advantages & limitations of different form factors, as well as all the variants.
If you have any specific questions after reading the overview, feel free to post again.