Precision is the ratio of the observation classified as positives that are actually positives. In binary classification settings, it takes the number of TP and divides it by the sum of TP and FP:
$$ \mathrm{Precision} = \frac{TP}{TP + FP} $$While recall uses in the denominator the total number of observations that are actually positives, precision uses the total number of observations that are classified as positives.
This metric is useful in cases of class imbalance and when the false positive creates severe inconvenience, financial loss or user distrust; a typical task where precision is used as a metric is spam detection.