A DAW, which stand for Digital Audio Workstation, is software used for the recording, editing and mixing of digital audio. DAW's started off as integrated hardware units but nowadays, a DAW most commonly refers to recording software.
DAW's follow many conventions from hardware recording set ups. You even have a virtual mixer console and can route audio similarly to hardware set ups. You can also process individual audio tracks using plugins such as EQ, compressors and reverbs.
Today's DAW's are very feature rich and most now also include things such as MIDI sequencers, video timelines, etc, alongside their core audio capabilities.
Ardour and Qtractor are two popular Linux DAW's.