Maximum a Posteriori Estimation
You can think it as an advanced version of maximum likelihood estimation (MLE). In MLE, we assume the parameter \boldsymbol\theta is a constant value. However, in maximum a posteriori (MAP) estimation, we assume the parameter \boldsymbol\theta is also a random variable.
Instead of maximizing p(\mathbf X\mid \boldsymbol\theta ), we would like to maximize the posterior p(\boldsymbol\theta\mid \mathbf X ). The meaning of the posterior here is that given the samples \mathbf X, the probability for the parameters to be \boldsymbol\theta.
As you see, we explicitly modeled the prior for \boldsymbol\theta as p(\boldsymbol\theta).