This is what my research skills book mentions:

The first few hundred cases selected using simple random sampling normally consist of bunches of cases whose numbers are closer together followed by a gap and then further bunching. For more than a few hundred cases, this pattern occurs far less frequently. Because of the technique’s random nature, it is, therefore, possible that the chance occurrence of such patterns will result in certain parts of a population being over- or under-represented.

I don't fully understand this. Can anyone explain better? Maybe with an example if possible?

Not so clear text ... maybe they wrote about the following example:

If the mean of each range (probability * sample size):

probabilities:

0.01, 0.03, 0.05, 0.08, 0.09, 0.1, 0.11, ...

Averages of small sample size: (10)

0.1, 0.3, 0.5, 0.8, 0.9, 1 , 1.1, 1.3, 1.6, 1.9, 2.1, 2.5, 3, 3.5, 3.8

You may get something like (with gaps):

0, 0, 0, 1, 0,1 ,0, 1,1, 0, 2, 0, 2, 3, 2

Averages of large sample size (10,000)

100 ,300, 500, 800, 900, 1000

You may get the following without gaps

95, 345, 477, 766, 921, 1011