On a computer diskette or hard disk, a sector is one of the "pie slices" the diskette or disk is divided into. Dividing the circular medium into pie slices is a way to organize it so that data can be located by the read/write heads of the drive. The diskette or disk is also divided into a number of concentric circles. Data can be located by knowing the number of the sector and the concentric track that passes through that sector. Each track is divided into a number of clusters that represent the smallest unit of storage that is addressable (can be written to or read). Typically, a cluster is 256 or 512 bytes in length.
Sector 0 of the diskette or disk contains a special file, the file allocation table (FAT). The FAT tells where the directory to the files on the medium is located and information about how clusters are used. You can't look at sector 0 directly.
On hard disks, the first sector is called variously the master boot record, the partition sector, or the partition table. This record or table tells how and whether the disk has been divided into logical partitions (for example, you can divide your hard drive into two logical partitions or drives so that you can load different operating systems on to the disk and switch back of forth). When your operating system is being booted or loaded into RAM, a program in this partition sector briefly gets control, determines how your disk is partitioned, and then reads the operating system boot sector and gives that boot sector program control so that the rest of the operating system can be loaded into RAM. The partition sector is the sector that can be "infected" when you leave a diskette in drive A that contains a boot virus.
The sectors as well as the rest of the organization of the diskette or disk are set up as a result of the process called formatting. Most diskettes you buy today are already formatted. However, if you're using an old one, you may need to reformat it. You can do this using a common utility that comes with your operating system.