Extended File Allocation Table, short for exFAT, is like an upgraded version of FAT32 and allows users to store files much larger than the 4GB allowed by FAT32. Files on an exFAT drive can be maximum of 256GB.
As for the compatibility, it works with all versions of Windows and modern versions of Mac OS X. It is one of the best partition formats of USB. So if you want the device you use supports exFAT, you should format all of them with exFAT.