Sound, in its most basic form is simply a vibration that can be heard. These vibrations are referred to as sound waves. The bigger they are, the louder they are and vice-versa. The time that it takes for a sound wave to repeat itself is referred to as frequency. Slower frequencies are lower in pitch and faster ones are higher in pitch.

Digital recording is a way of capturing sound for playback at a later time. It is achieved by using a microphone to detect sound and an analog to digital audio converter (ADC) to capture it. The ADC takes thousands of snapshots of a sound every second. The amount of snapshots taken per second is referred to as the sample rate. The resolution of each sample is referred to as bit depth. Higher sample rates and higher bit depth produce higher quality recordings.
One way to think of digital audio recording is in terms of digital photography. If you were to take consecutive snapshots of a ball rolling down a hill, the amount of snapshots you took of the ball would be the sample rate. The number of megapixels your camera has would be the bit depth.
A final thing to consider when it comes to recording sound digitally is signal level. A weak signal will add a noise floor to your recordings and an over driven signal will cause 'clipping' and result in a harsh distorted signal. Always set levels to be as healthy as possible without clipping.