A DAW, short for digital audio workstation, is essentially a single piece of software that acts as a MIDI sequencer, multitrack recorder, and mixing desk.
As home computers' processing power and storage increased, merging together MIDI sequencers and multitrack recorders became inevitable. By the early 1990s, the successor to Creator and Notator, Notator Logic, had migrated from the Atari ST to the Apple Mac. So had its main rival, Cubase. Both MIDI sequencers added multitrack recording, becoming Logic Audio and Cubase Audio respectively. Meanwhile, the successor to multitrack recorder Deck, Pro Tools, added MIDI sequencing.
Replacing the separate MIDI sequencer, multitrack recorder, and mixing desk with a single integrated program also removed the clutter and complications of getting all three physical devices to talk to each other. You no longer had to use a synchroniser to stripe a tape with a MIDI clock or MIDI time code. Moving the playback head to a certain point in a song inherently did so for both the MIDI notation and the audio recordings.
Being software that takes advantage of a computer's high resolution screen, DAWs also tended to show everything in a very visual and intuitive manner. You could see the waveforms, something you couldn't easily do with tape, and you could see them right next to the MIDI notes, side by side on the same screen.
With the advent of plug-ins, DAWs even replaced synthesisers and outboard gear, effectively becoming an entire self-contained studio.
This was arguably a double-edged sword, as instead of focusing on one discrete task at a time, you could go back and forth between composing, arranging, recording, and mixing. While it was useful that you could do this, if you weren't careful, it may have gotten distracting to the point it got in the way of your workflow.
MIDI: Atari ST MIDI sequencer timeline | DAW | Editor/librarian | MIDI | MIDI clock | MIDI sequencer | MIDI timing | Song position pointer | SysEx file
Types of sequencer: Analogue step sequencer | DAW | Digital sequencer | Digital step sequencer | MIDI sequencer
Types of software: DAW | Editor/librarian | MIDI sequencer | Tracker