Accuracy is the degree of closeness that a measured or calculated value has to the actual or TRUE value.
Precision expresses the proximity that a set of data points have to each other or the reproduciblity of a measuerment.
I you continue to make measurements and they agree with each other then the experiment is very precise. However it may not be accurate. Your data could be tighly grouped but far from the True value. Many years ago the physics department received some metersticks that started at the 1 cm mark rather than at 0 cm. Measuring with these meter sticks therefore always resulted in a distance that was approximately 1 cm short. You could easily measure repeatably to a few mm. The precision of the meter stick was therfore a few mm but the accuracy was about 1 cm.