I'd like to add a little to Superdesk's answer about the Kalman filter. Superdesk gives a great practical description; I'd like to add a more theoretical characterisation: the way I like to think about the Kalman filter. It also leads to an interesting bit of historical trivia about the Kalman filter that I don't think many people know.
The classical Kalman filter assumes that the observations of the parameters of the system model described in Superdesk's answer belong to a Gaussian random process. The aim of the Kalman filter is to estimate the parameters of these hidden Markov processes and to update the parameter estimates with their maximum likelihood values (i.e. the values that maximize the a prior probability of observing what is actually observed) with each new measurement.
Now imagine you have a model of a process - a driving car as in Superdesk's answer. You could simply take the car's whole sensor output history at each sensor as well as your model and brute force compute the parameters that give the maximum likelihood. You'd be doing the same thing as the Kalman filter, but this is NOT the Kalman filter. You'd also be doing a huge amount of number crunching, with an increasing workload at each step as your histories get longer and longer. It would be an impractical approach, especially in the early Apollo missions!
No, the point of the Kalman filter as opposed to general, brute force maximum likelihood estimation is that, as each new measurement comes in, the parameters of the (assumed) Gaussian probability distribution functions are updated by simple recurrence relationships that make use of former parameter estimates of these parameters and the new observation ALONE. You don't have to go back and get all the old observational data and do a maximum likelihood estimate from the newly augmented full dataset from scratch. So the Kalman filter is a maximum likelihood estimator, but it achieves this with vastly less computation than brute force maximum likelihood estimation.
Indeed, the Kalman filter was invented to drastically reduce HAND statistical calculations. For, even though we credit Rudolf Kalman with its invention, it was in fact invented by the great mathematician Carl Friedrich Gauss and first published by him in 1809, 150 years before Kalman. Gauss used the Kalman filter to simplify hand calculations needed to find optimal estimates of planetary orbits from astronomical observations. You can see that a simple recursive algorithm involving only the parameter estimates and most recent data would make hand calculation practicable: brute force maximum likelihood estimation would have been impossible. Kalman was unaware of Gauss's work, and indeed his method of proof that the simple algorithm is indeed maximum likelihood was quite different.
Kalman actually only found respect and credit for his work when he proposed it to Stanley_F._Schmidt and the latter led to the Kalman filter's adoption as a key path estimator during the Apollo missions.
See this exposition, "Recursive Estimation and the Kalman Filter" in D.G.S. Pollock's "Kalman Filters" on the history.