The process of converting analog signals
into digital information
The waveforms of the analog signal are sampled a particular amount times per second, and those samples are stored as binary data. Exactly what information (and how much of it) is in a particular sample depends on what is being digitized and at what quality the digitizing is being done.
The audio encoded on a CD, for example, has been sampled 44,100 times per second (i.e. at a sample rate of 44.1KHz). Digital Audio Tape (DAT) often uses a sample rate of 48KHz. DVD audio has a sample rate of 96KHz. Obviously, the higher the sample rate the "closer" to analog the signal is, as more of the original waveform is represented in the data.
The sample rate of digital audio affects the frequency range of the encoded audio. To adequately cover the approximately 20Hz-22KHz range of human hearing, the sample rate must be double the highest frequency (making it impossible to "miss" frequencies higher than the sample rate). Hence the 44.1KHz standard.
Digital audio samples feature varying bit sizes, which affect the maximum dynamic range of the sound. CD audio is genrerally 16 bit. Lower bit sizes decrease the possible dynamic range sampled; higher bit sizes increase it.
The concept behind digitizing video is similar, but as there are massively more data to deal with digital video is often highly compressed.