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.
#3
SGT
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.