Form Factor is the physical size and shape used when creating components for computers.
In essence each form factor allows for a different size or orientation by design. Generally larger form factors support any size below them.
There are several form factor types but the three most common types are MATX, ATX and BTX.
MATX or Micro ATX is the smallest design size. Using motherboards and cases with this design allow for the smallest PC footprint on your desktop.
ATX is todays standard PC box. This generally include Mid ATX and Full ATX sizes.
Last is BTX. This design is the newest on the market and still has yet to become mainstream. This case is very different from ATX. Its engineered in such a way to control the air flow throughout the case. In theory this design when combined with a BTX motherboard improves air circulation and helps keep temperatures down.