Hi,
You are totally right, a capacitor resists changes in voltage. In other words, the capacitor try to keep constant the voltage between its input and output. Consequence: When a voltage vary with time at the input, the output voltage will vary in the same way to maintain the voltage drop constant between input and output. So the varying signal will be transmitted from input to output.
When the variations are not so quick, the capacitor have time to discharge (so, it does not maintain voltage difference between input and output). So, DC voltages is cutted between input and output.