Looking back at the voltage divider, it is a circuit where the voltage
across the second resistor is proportional to the ratio of the second
resistor divided by the total resistance of the divider. Since ohms are
used for the calculations, we can replace the second resistor with a
capacitive reactance & still get the same results.
In a purely resistive voltage divider, when both resistances are equal
results in an output voltage that is half. With a reactance, there's a
frequency that will set the reactance to be equal to the resistance,
thus only half of the alternating signal will be available for further
processing.
There's another widely used frequency where the signal starts to be
noticeably attenuated if seen from the output of the divider. This
frequency corresponds to the point where the reactance will cause an
output of about 70% (0.7071x approx, which is the square root of 1/2) of
the original signal being delivered to the output; this frequency is
called the cutoff frequency.
The cutoff frequency in a filter is used for both blocking higher or
lower frequency signals. If blocking lower frequencies you can think of
it as the point where the filter start to conduct a large portion of the
input.
This basic circuit is the basis for most passive filters. One of the
disadvantages of this simple design is that it only allows for
attenuation of a signal, but other times it is of more use to amplify a
given range of frequencies & block others, instead of just
attenuating.
