Random errors are produced when measurements give readings that are either higher or lower indisciminately and with equal probability. The effect of random error can be reduced by repetition.
One example of random error is gauging the end-point of a titration. When using methyl orange as an indicator the colour change is from yellow to pink, with the endpoint being a shade of orange. It is difficult to be consistent about the exact end-point in these circumstances.
Reduction of random errors
If the inaccuracy is truly random there is an equal possibility of the measurement being greater than or less than the accepted accurate value. Repetition in this case would be likely to give an average closer to the 'actual' value than any specific reading.