Abbreviation for File Allocation Table. The FAT is a special file located on a disk containing information about the sizes of files stored on the disk and which clusters contain which files. It can also keep track of bad spots on a disk so they are not used. Think of it as a sort of roadmap to the files on a disk. Drives must first read the roadmap before they can find any of the information stored, or before they can know where to store any new information. There are a number of different types (formats) of FATs used that have different capabilities in terms of how (and how much) data can be stored on a drive partition.
While you don’t hear the term much these days the word “fat” has also been used to describe Mac programs that are capable of running in the older, non Power PC environments (68000 series processors) as well as newer PPC computers (600 and G series processors). They were called “fat” programs because they were bloated by virtue of having two sets of code, one for each environment.