Perhaps an analogy might be constructive.
Consider a submarine commander with a fat tanker in the cross hairs of his periscope.
He needs to shoot his torpedoes, not at where the target is now, but at some place where the torpedo will intersect with the target.
A skilled commander will have knowledge about how fast or slow the tanker can go. knowledge about how it turns, ect. This is the model.
Looking through the periscope, the commander tries to determine the position, speed, and heading of the target. These are the states of the model. A measurement of the state of the target is less than ideal through a periscope. The commander must make an educated guess of the state.
The commander “predicts” where the target will be and shoots his torpedo. After the expected run time, he raises the periscope and assess the scene. The torpedo ran ahead of the target and missed. The commander decides he had the speed too fast, and the heading was further away. He mentally updates his estimate of the state of the target.
The process repeats with a new attack.
A Kalman Filter doesn’t shoot torpedoes but does use the difference between what the state of the model predicts, and uses the error between the prediction and the measurement to update the estimate of the state.
Ideally there is a “true” model and it’s state is estimated in these recursive “predict-measure-update” cycles.
Typically, models are first order and can produce useful predictions over small steps.