Accuracy
Accuracy is how close a measurement is to the true or accepted value; it depends on calibration and freedom from systematic error.
Definition
Accuracy is how close your measurement is to the real answer; an accurate measurement hits the target. It is the closeness of a measured value to the true or accepted value, limited by systematic error such as an uncalibrated instrument or a flawed method, checked by measuring a known standard, and usually expressed as percent error. Because bias affects every trial equally, accuracy cannot be improved by repetition; it is established only by comparison with a reference standard, by calibration, or by agreement between independent methods. In formal metrology accuracy is a qualitative concept, and trueness (closeness of the mean to the reference) together with precision defines the overall uncertainty.
Example
A cup of water really has a mass of $100\ \text{g}$; a balance reading $99\ \text{g}$ is accurate, while one reading $85\ \text{g}$ is not, even if it reads $85\ \text{g}$ every time. A class measures water density as $0.97\ \text{g/cm}^3$ against the accepted $1.00\ \text{g/cm}^3$, a percent error of $\frac{|0.97 - 1.00|}{1.00} \times 100\% = 3\%$, and checking the cylinder against a known $50.0\ \text{mL}$ standard shows it reads $1.5\ \text{mL}$ high. A digital balance reading $0.30\ \text{g}$ with the pan empty makes a $13.50\ \text{g}$ rock really $13.20\ \text{g}$ and shifts its density from $2.70$ to $2.64\ \text{g/cm}^3$; taring before each measurement removes the bias without changing precision at all.
Key Insight
Accuracy is about being right, not about being consistent; a stopped clock is consistent but not accurate. Precision is how close repeated measurements are to each other, accuracy is how close they are to the truth, and you can have either without the other. The most dangerous measurement is precise but inaccurate, because its consistency looks like reliability, so calibrate against a standard before trusting any instrument no matter how repeatable it seems.