A consistent estimator is an estimator with the property that the probability of the estimated value and the true value of the population parameter not lying within c units (c is any arbitrary positive constant) of each other approaches zero as the sample size tends to infinity.  For example, consider a population mean of 10 and an interval of 1 unit either side — the interval from 9 to 11.  As samples get larger, the probability that the sample mean will fall outside that interval diminishes, and approaches zero when the sample gets large enough.  For a smaller interval, it takes longer for the probability to approach zero.