A term first used in the 1980s to describe early ‘tapeless’ recording/sampling machines like the Fairlight and Synclavier.
Nowadays, DAW is more commonly used to describe Audio+MIDI ‘virtual studio’ software programs such as Cubase, Logic Pro, Digital Performer, Studio One and such-like. Essentially it is elaborate software running on a bespoke or generic computer platform which is designed to replicate the processes involved in recording, replaying, mixing and processing real or virtual audio signals.
Many modern DAWs incorporate MIDI sequencing facilities as well as audio manipulation, a range of effects and sound generation and some offer integrated scorewriting (such as Apple Logic Pro and PreSonus Studio One v5's Score View).