Hard disks were not used in micro computers, so that any consideration of capacity much larger than the then-current floppy disks did not need to be considered, although there was room for expansion as we shall see. In fact the first IBM PC floppy disks held 160 K bytes on one side only. And each sector holds 512 bytes. If you divide 160 K bytes by 512 you find that there would be 320 sectors of storage area. In addition the FAT has space to keep other information as we shall see.
Lets step back a bit and look at what happens when a file is written to a disk.
First, the OS looks in the FAT to find an available sector. The number of this starting sector is recorded as part of the information kept along with the file name and some other data in the Directory Area. Usually of course this will be the next numbered sector, but not always. The number of the second sector is recorded in the FAT area of the first sector, to provide a link. The number of the third sector is recorded in the FAT area of the second sector and so on until the file is completely written to the disk.