How does oversampling improve the measurement precision?
If you had two identical recordings of a piece of music both with their own background noise (assumed to be non correlated) and you added numerically those two recordings together, the music amplitude would increase by 6 dB (assuming you got things exactly aligned) but, because the noises are uncorrelated the resultant noise amplitude would be only 3 dB larger. This is because uncorrelated noises add like this: -

$$N_T = \sqrt{N_1^2 + N_2^2}$$

That's a signal-to-noise improvement of 3 dB.

In effect, the scenario above is the same as sampling a noisy signal twice. You get a 3 dB improvement in SNR. If you sampled 4 times you'd get a 6 dB improvement in SNR. If you sampled 16 times you'd get a 12 dB improvement in SNR.

Another name for this is dithering.