Analog is simply an electronic signal that varies continuously in correspondence to an acoustic sound. Some kind of transducer, such as a microphone or a guitar pick-up, begins the process by turning the acoustic sound into a voltage. This voltage is then carried down a cable to a mixer, an amp, or some kind of recording device. An analog tape machine, such as a cassette, simply changes the signal into a corresponding magnetic signal which is recorded on a tape. This simply means that, at regular intervals, the voltage is measured and assigned a number.
Bit depth refers to the quantity of ones and zeros used in each sample.
The higher the bit depth, the more accurate the sound is. A standard audio CD has a bit depth of 16. Sample rate refers to how often the voltage of the analog signal is measured. One of the rules of digital audio is that the highest frequency you can record digitally is exactly half of the sample rate. So, if you are using a sample rate of 48 kHz, then the highest frequency you can record is 24 kHz.