A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].
An estimator is a function $W(X_1,...,X_n)$ of a sample. The realization of an estimator is called an estimate (Casella and Berger, 2002). Often, but not always, interest lies in a certain parameter for which the sample analogue is usually a good estimate in simple cases. For instance, the sample mean usually is a good estimate of the population mean. More complex problems require finding estimators in a more methodological way. There are several methods for this purpose such as the method of moments, maximum likelihood, or expectation maximization algorithms. Estimators can be compared based on properties such as bias, variance, mean squared error, consistency, asymptotic distribution, and admissibility.