FAT stands for File Allocation Table and basically it's a file format. The link I have provided below provides a very easy explanation with advantage and disadvantages of both.
http://technet.microsoft.com/en-us/library/cc940351.aspx
Modern versions of Windows support and recomends NTFS (New Technology File System). If you go about 3 quarters down the page on the link below it gives you a simple explanation with pros and cons.
http://support.microsoft.com/kb/100108