Resolution of Oversampling Converters
Suppose you have a signal which is 1/4 they way between LSBs.  With four noiseless samples you would just get four zeros.

With a slightly noisier signal, one fourth of those samples (1 on average) would actually get high enough to become a 1.  The average of three zeros and a one becomes 1/4.

Similarly if it were closer to 1, you would get some smaller fraction of 0s.