For an estimator $\hat\theta$ of a true parameter $\theta$, the mean squared error (MSE) is the expected squared distance between the estimate and the truth:
$$ \text{MSE}(\hat\theta)=\Bbb E\left[(\hat\theta-\theta)^2\right] $$
It measures the estimator’s overall error across repeated samples. Squaring ensures positive and negative errors do not cancel out, and penalizes larger errors more heavily.
MSE decomposes into variance plus squared bias:
$$ \text{MSE}(\hat\theta)=\text{Var}(\hat\theta)+\text{Bias}(\theta)^2 $$
So a good estimator has low MSE, not necessarily zero bias. A slightly biased estimator can outperform an unbiased one when its reduction in variance is larger than the added squared bias.