Why is the concept of a "state covariance matrix" necessary in estimation?
A resistance isn’t a particularly dynamic state, should be an unknown constant, but you might have a bin of resistors where they might vary. Taking one “randomly” out the bin makes it a random variable.  The bin of resistors will have a mean value, so perhaps that mean constitutes a state variable.  Perhaps someone starts putting resistors in the bin from a different source where they tend to run high, so the mean changes.

You don’t “have” to assume that the state is random if the model isn’t really random. Later you will find out in your class that states do not have to be stochastic. The KF equations will work for deterministic states. The measurement does need to have noise. If it doesn’t have measurement noise, you use a state observer, not a KF. 

A random state is actually very general and modeling errors are often successfully considered noise. 

Typically we use states because they encapsulate all the previous states. You use the current state to move to the next state. you don’t need to consider any past states to go to the next state. Some people will say a state has memory. If the state is stochastic, it has the Markov property. Your measurement depends only on the current state. 

The idea of randomness has many interpretations. It is part of what makes the topic interesting.