These cause readings to be spread about the true value, due to results varying in an unpredictable way from one measurement to the next.
Random errors are present when any measurement is made, and cannot be corrected. The effect of random errors can be reduced by making more measurements and calculating a new mean.
Random errors may be caused by human error, a faulty technique in taking the measurements, or by faulty equipment.
e.g. Rachael and Ricky are both timing a very fast pendulum with a stopwatch. Rachael can't count the swings accurately as it is just too fast to keep up - this introduces a random error in her readings as she may think she's counted 20 swings when in fact it was 21.
Ricky doesn't use the stopwatch very well. Although he starts it fairly accurately, he panics when having to stop it and is either too early or late. This is a random human error.