Improving Digitization by Adding White Noise Before Oversampling
Adding uncorrelated (i.e. white) noise to an analog signal prior to digitization is called dithering.
To understand why we would do this we need to understand the idea of quantization noise.
Consider an analog system which has signals ranging in amplitude from 0 to 100.
Suppose we digitize this signal with a digitizer whose digital levels are spaced by 1.
In other words, the possible digitized levels are

$$\left\{ -100, -99, -98 \ldots 99, 100 \right\} \, .$$

Now suppose the analog signal $s(t)$ is a DC signal of value 0.8, in other words

$$s(t) = 0.8 \, .$$

If we put this into the digitizer, the digitizer will round it to 1 and our digital samples $s_n$ will be

$$s_n = 1\,.$$

This is not good because now the our digital signal accumulates error as we acquire more signal.
The digitized level is always too high so the longer we average the signal the more we over-estimate the analog level.

Adding white noise helps fix this problem because it pushes the analog level around such that it crosses neighboring digitization levels.
Therefore, as  you average over a set of digitized values you actually get something which is close to the true analog level.
Let's see this via example.

Suppose the noise we add is Gaussian distributed with $\sigma=2$.
Then the distribution of the analog signal is

$$p(x)
\propto \exp \left[ \frac{-(x - s(t))^2}{2\sigma^2} \right]
= \exp \left[ \frac{-(x-0.8)^2}{8} \right] \, .
$$

We now compute the average digital value $\langle s_n \rangle$ by averaging $p(x)$ over the integers.
The normalization constant for the distribution is
$$N = \sum_{m=-100}^{100} \exp \left[ \frac{-(m-0.8)^2}{8} \right]$$
and so we have
$$\langle s_n \rangle =
\frac{1}{N}
\sum_{m=-100}^{100} m \exp\left[ \frac{-(m-0.8)^2}{8}\right] = 0.79999\ldots$$
Thus you can see that adding the white noise caused the average digitized signal to more closely match the true analog value.

Of course, adding the noise makes your signal to noise ratio worse.
That means to to actually have a high probability of measuring the $\langle s_n\rangle$ we just computed, you have to take more samples than you would think in the noiseless case.
This is why you hear about over-sampling and dithering at the same time.
Because the dithering noise is truly uncorrelated, taking more samples always helps improve the signal to noise ratio, even if you're sampling way above the bandwidth of the analog signal coming in.