The Atari TT was a kind of a super Atari STe. As the other Atari computers, it was very long awaited. It was presented as a competitor of the Macintosh and was one of the first to offer a huge graphic resolution (1280 x 960).
The first TTs had a 16Mhz CPU. A small daugther card was supplied later to use a 32 MHz CPU, then all the TTs were shipped with a 32 MHz CPU.
It had a lot of extension connectors (like VME, VGA or SCSI) to allow it to be connected to a lot of standard peripherals.
It had also several features of the Atari STe, like the sound system, but contrary to this one, it didn't have its enhanced video features (fine scrolling) and its Blitter (custom chip designed to move bitmap blocks).
It had, like the Amiga computers, a special memory organisation : 4 MB, expandable to 12 MB (called ST RAM) was used for coprocessors (video, sound, ASCI) and the rest (called TT RAM which can be located on the motherboard or on a VME card) was used only for 68030 processor and wasn't slowed by peripherals accesses. Both SCSI and serial could do DMA transfers directly to TT-RAM.
A special version of the TT was designed to be a UNIX station, called TT/X it was supplied with UNIX System V R4 and WISH (an extension of OSF Motif).
However the TT and the TT/X had no success and there was no (or so few) software especially designed for this computer. Notice that a Macintosh emulator (called Spectre GCR - done by Dave Small-) turned the Atari TT into a very fast Macintosh clone : Macintosh software could be used on the TT, and often they ran faster than on the original Mac!)