Layman Description of the Kalman Filter
KF is actually a mixture of a deterministic state propagator and a statistical estimator.

Despite it's name including the term filter, Kalman filter is not a simple frequency selective one. It's indeed a statistical recursive estimator of a state of a (linear) dynamic system. Yet on a broader sense it's called as a filter as it will separate a desired signal (the state) from corrupted measurements; hence filtering.

A linear dynamical system (LDS) is a physical construct whose behaviour is described by (linear) differential equations; 

$$ \dot{X} = A X + Bu + W $$

where the vector $X$ is the state of the system, the matrix $A$ is the state propagation information (derived based on the differential equation of the LDS) , $u$ is a vector of deterministic inputs and $W$ is the state noise; depicting the uncertainity in the LDS propagation model $A$.

KF takes advantage of this deterministic behaviour of a LDS before estimating the current state $X$ purely from noisy measurements. 

$$ Y = C X + Du + V $$

where $Y$ is the observation about the system and $V$ is the measurement noise on it.

Given a previous estimate of the state, it first deterministically propagates this previous estimate into current estimate through the matrix $A$ (process equation), and then performs a new finer estimate on the difference of the current measurement and propagated estimate using the measurment equation.