FAT stands for "File Allocation Table", and it is a hidden file used by the File System to keep track of which sectors of a HDD are allocated to which files, and where is the next sector in this file? The "16" means the entries in the FAT are 16 binary bits long, which sets a limit on the maximum number of sectors it can track, and hence a limit on the size or HDD it can be used on.
As hard drives got larger, FAT 16 became outmoded long ago because they could not be used on larger drives. In fact, the most recent version of that system, FAT32, is now considered too small for today's drives. So nobody uses FAT16 for anything these days.