Intuitive explanation for filters
I'm not sure if this is considered intuitive or not, but I suppose we'll see!

Simple RC/RL filters are fairly intuitive once you grasp the basic response of capacitors and inductors to signals of various frequencies, which you clearly do.
Capacitors act as (mostly) open circuits to low frequency signals, and (mostly) short circuits to high frequency signals, while inductors are the opposite, and readily pass low frequencies but block high.

This can indeed be seen by their reactances, XC for the capacitor and XL for the inductor:

$$X_C = \frac{1}{\omega C} $$
$$X_L = \omega L$$

where ω is the angular frequency of the signal. Clearly, the capacitor's reactance grows as ω shrinks, and vice versa.

Let's connect a capacitor to a resistor:
  

As per above, for low frequency signals, the capacitor will act like an open circuit, and most of the input voltage will drop across it, so the filter passes them (if output is taken at the port to the right).
For high frequency signals, the opposite is true; the capacitor acts like a short circuit, which leads to it have little to no voltage drop across it, so these frequencies are attenuated by the filter.


In an RL circuit, the inductor will drop little to no voltage for low-frequency signals, so these signals will become attenuated. As the signals increase in frequency, the inductive reactance becomes a larger factor, so more and more of the signal is passed on to the output port.

And, of course, we can switch the position of the two elements, and take the output across the other one, to make both low-pass and high-pass RC filters, and likewise for RL filters.

... Though I suspect you know as much, if you know reactance.