Cardioid microphones are so named because the sensitivity pattern is heart-shaped, i.e. a cardioid.
Cardioid microphones are commonly used as vocal or speech microphones because they are good at rejecting sounds from other directions. In three dimensions, the cardioid is shaped like an apple centered around the microphone, which is the "stem" of the apple.
The cardioid response reduces pickup from the side and rear, helping to avoid feedback from the monitors. Since these directional transducer microphones achieve their patterns by sensing pressure gradient, putting them very close to the sound source (at distances of a few centimeters) results in a bass boost due to the increased gradient. This is known as the proximity effect. The SM58 has been the most commonly used microphone for live vocals for more than 50 years demonstrating the importance and popularity of cardioid mics.
The cardioid is effectively a superposition of an omnidirectional (pressure) and a figure-8 (pressure gradient) microphone; for sound waves coming from the back, the negative signal from the figure-8 cancels the positive signal from the omnidirectional element, whereas, for sound waves coming from the front, the two add to each other.
By combining the two components in different ratios, any pattern between Omni and figure-8 can be achieved, which comprise the first-order cardioid family.
Common shapes include: