We want estimators to be:

Unbiased  -- The expected value of the estimator is the same as the parameter it is estimating.

Consistent  -- As the sample size increases, the estimator gets closer to the parameter.  (Proper definition:  consistent estimator.)

Efficient (or relatively efficient)  -- The estimator you're using is at least as good as any other estimator. (Proper definition: efficient estimator)