ATX is a form factor.
Just as AT and BTX are other form factors
AT is the old form factor for PC's...
ATX is the current widespread used form factor for PC's...
BTX will be the new form factor of the future...
(all have sub form factors, like babyAT, microATX, microBTX, etc)
A form factor defines how and where things are placed and what the dimensions are. It describes the general shape, what sorts of cases and power supplies it can use, its physical organization, etc. Thus so component A would fit in/on component B.
For example, a company can make two motherboards that have basically the same functionality but that use a different form factor, and the only real differences will be the physical layout of the board, the position of the components...
eg: a power supply with form factor ATX would not fit in a case with form factor AT or BTX. So make sure you buy the correct PSU with the correct form factor for your case and motherboard. This would mean an ATX one, unless you still have a stone-age PC or a ultra-super-modern PC.
http://www.formfactors.org/formfactor.asp