File Allocation Table (FAT) is the name of a computer file system architecture and a family of industry standard file systems utilizing it.

The FAT file system is a legacy filesystem which is very simple, but cannot offer the same performance, reliability and scalability that modern filesystems such as NTFS, ext4 and btrfs can offer. It is however supported for compatibility reasons by virtually all existing operating systems for personal computers, and thus is a well-suited format for data exchange between computers and devices of almost any type and age from the early 1980s up to the present.

Wikipedia has a large entry covering most of the aspects of FAT.