you have an analogue signal coming form a guitar or mic or keyboard which is fed into a device like a sound card (or an Input / output deice). The sound card then converts the analogue signal into a digital signal. This is then stored on the computers hard drive.

You can then play back the digital signal and have it converted into an analogue signal that a set of speakers or headphones can understand and play another track which you can also record (overdubbing).

And thats it really.

You can add effects like reverb and pan the signal from left to right until you have sounds form multiple instruments all playing nicely together at the same time.