Kalman filter system/measurement noise covariance

Question

This may be a bit of a dumb question, but the textbook I'm using doesn't do a deep dive into the intuition on each parameter of the Kalman filter. When I am devising my system model & measurement model, they both include a noise term. Take

s(k+1) = A * s(k) + N([0; 0], Em) -- system model (2x1)

zk = C * s(k) + N([0], Eo) -- measurement model (1x1)

where A is the transition matrix (2x2), C is the observation matrix (1x2), Em is the system noise covariance (2x2), Eo is the measurement noise covariance (1x1).

Now, N() is the normal distribution calculating the noise term, I presume. What exactly is N calculating? Is it a constant term added to every system transition & every measurement? Or is it a Gaussian random vector that adds some random noise (who's likelihood is bounded by the variance)? Is it a probability density function that transforms s(k+1) into a PDF itself?

Secondly, (assuming s(k+1) is not a PDF at this point) what does adding/subtracting to/from a measurement value do to benefit the ultimate prediction? To me, it seems like changing those values from the explicitly measured values would make the ultimate prediction less accurate.

Thanks for your help!