NTFS is New Technology File System, a type of file system
developed by Microsoft and it propriety (this means it's by Windows
ONLY). It's only used in Windows NT onwards (NT by the way stands
for New Technology).
One main difference between NTFS and FAT32 is that NTFS is a
Journaling File System. This means that data will be written to a
journal first (a special area in the hard disk) before the data is
written to the disk itself.
This makes recovery easier should the system crashes, by using the
previous stable state of data. This also eliminates the use of
Chkdsk, which is often the case in FAT32 systems if system
crashes.
To illustrate the point clearly, set up two Windows XP PCs, one
using NTFS, the other using FAT32.
Do a force shutdown (just turn off the power). Then turn it back
on. For NTFS, you will notice that Chkdsk doesn't run on startup;
Windows automatically revert it to the previous stable state.
However, for FAT32, Chkdsk will run, since there's no way to check
if the data has been written correctly to the hard disk.
If your system crashes too often and it's a FAT32 file system as
well, you may well find it near impossible to recover without ever
reformatting and reinstalling Windows.
Another major difference is the size of your partition. For FAT32,
the maximum it can go is 2TB. That means if you have a huge hard
disk, you probably will have lots of partitioning to do. For NTFS,
it's possible to format a partition that has more than 2 TB.
Another issue is the file size. Files on FAT32 cannot go larger
than 2GB. Files on NTFS can.
Disk compression is possible only in NTFS, not for FAT32, so is
encryption. Notice that these 2 options are missing in FAT32
partitions.
The last issue is the OS it supports. NTFS is only supported on
Windows NT and above, whereas FAT32 is supported by all OS. You
can't install Windows 98 on NTFS partition, but it's possible to
install Windows XP on a FAT32 partition.