Maximum a priori estimation (MAP) is the problem of selecting the value of a latent variable $y$ that maximizes the posterior probability given observations $x$:
$$ y_\text{MAP}=\argmax_y p(y\mid x) $$
MAP is MLE with regularization induced by the prior: if the prior is uniform ($p(\theta) = \text{const})$ then MAP reduces to MLE.
MAP corresponds to minimizing 0-1 loss:
$$ \ell(y,\hat y)= \begin{cases} 0 & y=\hat y\\ 1 & y\ne\hat y \end{cases} $$
Under this loss, the Bayes optimal decision rule is to choose the posterior mode. If the loss is different (e.g., Hamming loss), MAP is not necessarily optimal.