In statistical classification, the precision of a classifier over a class is the ratio between the number of times that class got predicted correctly and the number of times that class got predicted. Namely,
$$ \text{precision}(x) = \frac{N_\text{correctly predicted}(x)}{N_\text{predicted}(x)}, $$
where $x$ is the class being predicted.
Typically, this appears in binary classification, where we want to compare the number of true positives against the number of true and false positives.
See also Recall (classification), Accuracy (classification) and F-score.