Cutoff and the First-Order High-Pass
Highs pass, lows are blocked
The graph's horizontal axis is frequency on a logarithmic scale, and the vertical axis is the gain, the ratio of output size to input size. Raise the frequency from low to high: at first the signal is almost blocked, then it gradually gets through; find the cutoff frequency where the gain climbs to 1/√2, that is, −3dB. The lower tick on the vertical axis marks exactly that height.
This time the output is across the resistor
The low-pass filter took its output across the capacitor, but the high-pass filter looks across the resistor of the same series RC. At low frequencies the capacitor's impedance, 1/ωC, is very large, so it takes almost all the voltage and hardly any appears across the resistor. That is why low frequencies are blocked. As the frequency rises the capacitor's share shrinks and the resistor picks up the voltage, so high frequencies get through.
The cutoff frequency ω_c = 1/RC
Just as with the low-pass filter, the boundary is the frequency at which the resistance and the size of the capacitor's impedance become equal. That point is ω_c = 1/RC, and the output becomes 1/√2 ≈ 0.707 times the input, that is, −3dB. The sign of the phase is reversed, however: in the high-pass filter the output leads the input by 45 degrees, and the phase approaches +90 degrees as you go further below the cutoff.
Below cutoff it rises at a fixed slope
Above the cutoff the gain is nearly 1 and flat. Below the cutoff, every time the frequency drops tenfold the gain falls to 1/10, that is, by −20dB. This plot draws the gain itself on the vertical axis, but in a Bode plot drawn in dB, the corner where the flat line above the cutoff meets the line below it sloping at −20dB/decade (or +20dB/decade read going upward) is the cutoff frequency. High-pass filters are used to block the DC component and pass only the changes in a signal, as in differentiators and coupling capacitors.
Back to the first screen
As you raised the frequency, the gain started near 0, bent upward near the cutoff, and at exactly ω_c = 1/RC the output was 0.707 times the input, −3dB. Above that it flattened out toward 1. The very same parts as the low-pass filter, with the single difference of taking the output across the resistor, turned the passed frequencies exactly around.