As your cleverest professors might be fond of saying: "A measurement can be accurate without being precise; a measurement can be precise without being accurate." A simple demonstration of this distinction: We can refer to a wrapped collection of hay as a bale (an accurate measurement) without precisely counting its strands; we can scatter the hay and number the strands (a precise measurement) but not accurately call it a bale. More to the point, we cannot claim that a particular event occurred "precisely 20,000 years ago" or that a particular ore reserve weighs "precisely 1 million tonnes"; by definition, such values are measured coarsely rather than exactly. In relation to the weather, we would properly refer to an accurate (true) forecast, but a precise (exact) temperature.
"Accuracy" denotes how closely a measurement approaches its true value. An accurate measure, then, is one that conforms well to an implied or stated benchmark:
The accuracy of the test results was verified by running 50 of the samples a second time.
This particular scale is accurate to the nearest kilogram.
"Precise" means marked by a high degree of exactitude:
One pint is precisely 568.245 milliliters.
In the simplest terms, accuracy is about conformity to truth or fact, while precision is about exactness.
For an interesting look at the distinctions between "accurate" and "precise," visit these pages:
"Accuracy vs. precision demonstrated by rifle shots at a bull’s eye target [1]"
"What is the Difference Between Accuracy and Precision? [2]" article by meteorologist Jeff Haby