Precision is about variability while (in contrast to precision), accuracy is about bias.
Precision is a property of statistical estimators and of measurements.
Precision of an estimator is the degree of variability (scatter) of the estimates around their mean. High precision means low variability around the mean. Precision can be contrasted to accuracy; precision is about variability while accuracy is about bias.
Any statistical procedure to generate a numerical estimate or prediction is said to be precise when its sampling distribution has low scatter, typically measured as a variance. An estimator or forecast rule can be said to be accurate when a central value (usually, its expectation) equals the estimand or the central value of the target of the forecast, respectively. The two concepts are independent of each other, so a particular estimator or forecast rule can be accurate, precise, both, or neither.
For example, lack of precision (large variability) may result from a small sample on which the estimation or forecasting is based. Increasing the sample size alone may improve precision but does not necessarily improve accuracy. Meanwhile, lack of accuracy (large bias) may result from a systematic error. Eliminating the systematic error improves accuracy but does not necessarily change precision.
Statistical literature may prefer the terms bias and variability instead of accuracy and precision: bias is the amount of inaccuracy and variability is the amount of imprecision.
(Loosely based on Wikipedia's article "Accuracy and precision".)
In the context of measurements, accuracy is the tendency of the measurements to agree with the true values. Precision is the degree to which the measurements pin down an actual value.