Accuracy is the nearness of a measurement to the standard or true value.

Precision

Precision is the degree to which several measurements are close to each other.

Illustration

When target shooting, a high score indicates the nearness to the bulls-eye and is a measure of the shooter's accuracy. Precision is indicated by the tightness of the shoot grouping.

Sighting-in (or zeroing-in) is the process of improving the accuracy of your weapon by adjusting or compensating for any deviations in the manufacture of the weapon (as well as other external factors).

Example

If we measure a 1-foot ruler and get the values: 12.01 in
12.00 in
11.99 in
12.00 in
we deduce that the measurements are precise to +/- .01 inch, but we know nothing about the accuracy based on the information given.