Basically a digital audio workstation, refered to as "DAW", is a computer-based system of software programs, audio hardware and usually a variety of virtual, acoustic and/or electric instruments which are used collectively to record sound and music. Most home computers these days can pass as a DAW, but usually one needs a multitrack editing software program to make a computer function as a DAW. Turning a normal computer into a real DAW is less costly than one can imagine when thinking about a professional recording studio. You will need your computer with a fair bit of processing power - a Dual Core would probably be able to haul most of the workload creation in your recording and editing software.
Don't forget to purchase a quality sound card so that all of your analog audio signals (if you happen to be using microphones and electric instruments with a 1/4") into digital form. The MBox 2 coupled with protools has been a popular DAW amongst many home-studio producers. Also, Cakewalk Sonar coupled with E-MU Systems' digital audio stations have something like 16 inputs and 16 outputs so one could literally run an entire band's lines through recording software - thus a music producer can record a band's live performances, record individual members on separate tracks, and can mix and master from multitrack down to any audio file type. What is great about using computers as a DAW is that it is very easy to undo accidental erasings and bad takes. Traditional recording studios never made it easy as clicking the "Undo" button to get back to a previous state of work.
Quality sound in terms of a DAW comes down to the capturing source quality because converting from analog to digital is virtually seamless with a quality sound card. Quality control is important. Make sure your instrument cables are properly plugged in to your digital audio station. Also test the volume levels on your instrument AND also test out your instrument's sound in the software program by enabling recording. Doublecheck the audio levels of your recording line and also doublecheck that your recording source is properly selected. Your recording space should be an empty room somewhere quiet with no windows in order to limit latent noise from being captured. Invest in a quality microphone, pop-stopper and mic stand to prevent unwanted pops, clicks and static noise from holding and moving about with a mic. With the basics in line, your music hobby will establish a great foundation, especially with the experience and maybe someday you can take it to the next level and be a professional in some respects regarding a certain facet of the music industry.