The random error is the fluctuating part of the overall error that varies from measurement to measurement. Normally, the random error is defined as the deviation of the total error from its mean value.
An example of random error is putting the same weight on an electronic scales several times and obtaining readings that vary in random fashion from one reading to the next. The differences between these readings and the actual weight correspond to the random error of the scale measurements.
The opposite (or complementary) concept is systematic error. In contrast to systematic errors, the effect of the random errors may be reduced by repetition of the experiment or observation and averaging the outcomes.