I is the simplest, a sub-band coder with a psycoacustic model. Layer II adds more advanced bit allocation techniques and greater accuracy. The specs say that a valid Layer III decoder shall be able to decode any Layer I, II or III MPEG Audio stream. A Layer II decoder shall be able to decode Layer I and Layer II streams. Well, first you need to know how sound is stored in a computer.
Sound is pressure differences in air.
When picked up by a microphone and fed through an amplifier this becomes voltage levels. The voltage is sampled by the computer a number of times per second. For CD-audio quality you need to sample 44100 times per second and each sample has a resolution of 16 bits. To compress audio MPEG tries to remove the irrelevant parts of the signal and the redundant parts of the signal. Parts of the sound that we do not hear can be thrown away.