It is interesting that our ears obey a precisely logarithmic law when assigning subjective pitches to frequencies. Even though an octave is strictly speaking a subjective judgment, it is so closely equal to frequency doubling (no matter where one is in frequency) that it has been defined as an objective measure.
Tom, this is a fairly deep subject! Here are reasonably brief answers to your questions: Oversampling is used during the analog to digital (A/D) and digital to analog (D/A) conversion processes in a digital recorder, sampler or playback device. Essentially, the sampling rate of the converter is multiplied to a very high rate (i.e. 4x oversampling puts the rate at 176.4 kHz). This accomplishes two things: First, it allows the anti-aliasing and anti-imaging filters on the converters to be much more gentle, which reduces phase distortion. Second, in a 4x oversampled system, it results in a 6 dB drop in noise (other rates result in more or less noise reduction).
Tom continues, "I was talking with a co-worker about digital audio, and I told him that all audio CD's are in 44.1khz 16-bit stereo digital format, and if copied digitally, the audio will be identical when copied back to another CD... but he brought up oversampling, and said that if a CD is recorded with oversampling, a copy of this CD will be worse quality. What's the deal?"
In this case, your co-worker is incorrect (don't rub it in too much!). The data stored on a standard Red Book audio CD is 16-bits, at 44.1 kHz. While oversampling might result in a better A/D conversion when making the CD master, and an oversampling CD player might result in better D/A playback, this is a function of the converters, not the data on the CD. Digitally "cloning" that CD will produce an exact bit-for-bit copy. Since no conversion to analog is used, oversampling does not enter into the picture.