It is not always obvious what the best way to estimate a parameter is. For example, the sample mean and sample median are both natural estimators of the mean of a normal population. We want our estimator to be like target 3: unbiased with the smallest possible variance. Thus, we only look at unbiased estimators and choose the one with the smallest variance. This we call the minimum variance unbiased estimator/ (MVUE) or the best unbiased estimator/ (BUE), because it is the ``best'' estimator we can get using only unbiased estimators.
NOTE:\
For the normal distribution, the mean, median, and mode all occur at
the same location. Why do we usually use the mean, 
, instead
of the median, 
? It turns out that both and
are unbiased, but has a smaller variance than
. In fact, is the MVUE. See the ``Minimum
variance estimation''
concept lab for some examples of this.