A Parabolic microphone is a microphone with a parabolic reflector fitted to it. This collects and focuses sound on the microphones head like a TV dish picks up satellite signals. This has many advantages for picking up and amplifying distant sounds that you want to isolate from the rest of the environment. A classic example is bird song because parabolic reflectors are very good at picking up high frequencies. this is also used in sports broadcasting, eavesdropping and espionage.
The high frequencies are picked up more due to the direct physical laws of sound waves. This is because they only focus waves with a wavelength much smaller than the diameter of the parabola. To obtain hi-fidelity sounds including the lower end frequencies (down to 20Hz) you need a parabola around 17 metres. This is because if we say the speed of sound is 342 m/s through the air speed of sound 342 ms / 20 Hz = 17 metres. Parabolic reflectors will sacrifice the lower end frequencies to be more manageable sizes.
Representation of how Parabolic Reflectors works with microphone facing the central point for maximum pickup.