Truecrypt requires drivers because it operates on the block level.
The "block level" is required because mass storage devices do not understand anything about files, they only understand reading and writing blocks of 512 or 4096 bytes. (Most modern hard drives have an "LBA" number on the sticker. This is the highest block number for that drive.)
Consequently, there is a small software stack with regard to filesystems on most, if not all, operating systems. Application programs deal with files in terms of opening, reading, writing, and closing specific files. So, you'll have a "filesystem driver" that understands the specific filesystem being used, whether it's NTFS, FAT, ext4, or whatever. This filesystem driver translates those high-level operations to read/write requests for specific block numbers by invoking a lower-level "controller driver" that actually sends/receives commands to the controller of that specific device.
This is a Good Thing(tm) because an operating system can use the same filesystem software on any storage device.
Truecrypt sticks itself between the filesystem driver and the controller driver, intercepting blocks of data and encrypting/decrypting them before they are passed to the lower/upper layer.
Drivers operate in kernel mode with full access to the machine. Because of this some software uses drivers to accomplish tasks other than talking to devices, such as Belarc Advisor's BANTEXT driver.
So the designers of Windows wisely made it so that drivers can't be installed without administrative rights. Vista/7 takes this one step further and requires them to be signed with a Microsoft key.