Roughly speaking, they are the amount of noise in your system. Process noise is the noise in the process - if the system is a moving car on the interstate on cruise control, there will be slight variations in the speed due to bumps, hills, winds, and so on. Q tells how much variance and covariance there is. The diagonal of Q contains the variance of each state variable, and off diagonal contain the covariances between the different state variables (e.g. velocity in x vs position in y).
R contains the variance of your measurement. In the above example, our measurement might just be speed from the speedometer. Suppose it's reading has a standard deviation of 0.2 mph. Then R=[0.2^2]=[0.04]. Squared because variance is the square of the standard deviation.
Q is in state space, and R is in measurement space. In the example above, our state might be position only $[x, y]^T$, and measurement space is velocity $[v]$. That is problematic because that is not velocity in terms of x and y - you need the heading to convert. The Kalman filter matrix H is used to do that conversion, and in nonlinear systems you tend to have to linearize that in some manner.
Shameless plug: my free book on the Kalman filter goes into this in great detail: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python