In today's parlance, a DAW ("Digital Audio Workstation") is a computer program that's used to record, mix, and produce music, but I think the term originally referred to a physical workstation for working with digital audio (as opposed to analog audio).
Modern DAW software generally combines several types of functions-- recording and editing audio tracks, recording and editing MIDI tracks, transmitting MIDI data sequences to external devices to control them, playing virtual instruments, hosting third-party plugins, applying effects to audio and MIDI tracks, processing tracks in various ways (such as compression, filtering, and equalization), balancing the relative volumes and stereo panning of the tracks, and of course mixing everything down to a finished audio file.
Although a DAW can take the place of a recording studio, it doesn't necessarily do so. Rather, a DAW is frequently used in a recording studio along with more traditional audio devices and procedures. For instance, if you're recording a song then you'll still need someone to sing into a microphone, and you'll probably want them to be in a sound booth, or at least in a room with good acoustics and sound-proofing to keep out unwanted background noises. If you're a musician then you'll probably still want to play your physical instrument-- guitar, piano, violin, drums, or whatever-- and record the audio in the DAW. You might need a mixer to balance and mix audio coming from several different sources before you transmit it to the DAW for recoding. But if you don't have any physical instruments then you could use a DAW's virtual instruments, composing and performing an orchestral arrangement using just the computer, DAW, and any third-party plugins.