This is a name to denote the specifications of a motherboard - like dimensions, power supply type, location of mounting holes, number of ports on the back panel, etc. The most commonly-used motherboards are of the ATX or Micro ATX form factor, which are used for Desktop systems.
An ATX (Advanced Technology Extended) motherboard is 12" x 9.6" in size, and supports the most number of expansion slots. Micro ATX is shorter than ATX, at 9.6" x 9.6", and was created to reduce total cost. The original ATX specifications have been updated to include technological improvements and reconcile the requirements of later PCs. For example, the latest ATX form factor specification includes the 24-pin power connector, which the original did not. There are many other form factors that cater to different PC designs: BTX, ITX, mini ITX, FTX, and more. VIA, a computer component manufacturer that focuses on power efficiency, has been creating mini ITX motherboards, which include all the functionality of the larger motherboards. With all important functions - video, audio, USB, and LAN - on board the motherboard, there is need for only one PCI slot and a RAM slot, besides a socket for the CPU, usually a VIA processor that consumes less than 5 watts. Such systems are ideal for use in situations where the workload is low and where the systems need to be left running - like downloading very large files.