It is the optimal filtering technique to recover the maximum information
about a signal in the presence of noise.
It is used (for example) to extract the signals from distant space satellites
when they are covered up by lots of noise.
In addition of what Antiphon wrote:
When we say that some system is optimal, it is optimal relative to some parameter. Kalman filter is the optimal estimator for a linear system in the sense of minimization of the error covariance matrix.
The extended Kalman filter, is a suboptimal estimator used in nonlinear systems. for instance radar and sonar tracking systems. One important characteristic of the KF is that you can estimate velocity and acceleration of a dynamic system from noisy measurements of it's position.