DAT is Digital Audio Tape. It's a format with some similarities to VHS.
Maybe you mean DAW- Digital Audio Workstation. That would be either a standalone like the Boss/Yamaha/Akai etc or PC/Mac-based hardware and software solutions to recording and editing audio.
Digital formats store the information as 1's and 0's as opposed to analog tape that stores the information magnetically and in a linear fashion. The advantage of digital formats is in editing and in the ability to create copies without hiss and other artifacts that are inherent in analog tape formats. Some of the disadvantages of digital audio are the need for DA/AD converters that can add their own artifacts to the digital recording, the lack of "tape saturation" that many people find to be a pleasing element of analog, and the need to dither bit depth and resolution when recording in anything other than 16bit/44.1k before burning to CD.