Precision refers to the repeatability of the measurements, i.e., how close to the same quantity are multiple measurements. Random errors occur from uncontrolled sources. A good example would be the air currents surrounding a balance during a weighing. The resultant weights would fluctuate about a true value. A good example would be a damaged weight in a balance that would cause consistent readings different from the true value.
Significant Figures play an important part in scientific measurement.
These are digits that are known with certainty plus one uncertain digit. Measured numbers can never be known exactly. Defined numbers can be known exactly. A good illustration of a defined number is a dozen - twelve. By definition, exactly 12 make a dozen.