When introducing Windows NT, Microsoft needed a faster and more stable file system than FAT. NTFS uses clusters to store data as well but the clusters can vary in size minimizing the loss (FAT's clusters is locked to a specific size).
NTFS splits the drive into four theoretical parts. The first part, MFT (Master File Table), contains important information about the files, free space and so forth. Then comes an area that can be used for storage, until we reach the exact middle of the drive. Here a copy of the first 16 MFT-files are stored again, and then we have another area where you can store data.
NTFS can contrary to FAT, compress and encrypt data stored on the drive. It also has a much higher fault tolerance then FAT. NTFS has gotten a bad reputation as a rather slow file system. The truth is that it is rather memory reliant, so on system with 512 memory and up NTFS gets significantly faster. Unfortunately only NT-based Windows can read NTFS.
FAT exists in basically two flavors: FAT16 and FAT32. FAT16 holds cluster information based on 16 bits of information, and FAT32 uses 32 bits to manage the storage space. As a result, FAT16 can manage 65535 clusters and FAT32 can handle a maximum of 268435456 clusters, for a maximum storage capacity of 2GB and 2TB respectively. FAT16's maximum file size is 2GB while FAT32's maximum file size is 4 GB.
There have been going around a rumour that FAT would actually be faster than NTFS. This was true as long as your system was very poorly equipped with RAM, which happened at about the launch of Windows XP. Not only did the OS itself require a lot of RAM, 128MB, to run ok, but to be able to play games and such you needed at least twice that and NTFS had to take a lot of the fault for that. However as long as you use 256MB RAM and up NTFS is just as fast and even faster when you get past 512MB, which most people most likely have today