The term handheld microphone generally means any microphone that's supposed to be held in the hand while picking up sound. Handheld microphones are used in a huge variety of settings, from musical performances to television interviews.
A cardioid microphone has the most sensitivity at the front and is least sensitive at the back. This isolates it from unwanted ambient sound and gives much more resistance to feedback than omnidirectional microphones. This makes a cardioid microphone particularly suitable for loud stages.
Condenser microphones are more sensitive than Dynamic microphones. They use an electrically-charged diaphragm & backplate assembly to form a sound sensitive capacitor. When sound sets the diaphragm in motion, the distance between the diaphragm and the backplate changes. This variation in spacing changes the capacity of the capacitor, and produces the needed electrical signal. All condenser microphones need to be powered: either by batteries in the microphone or by externally provided phantom power.
A microphone with tailored frequency response is usually designed to enhance a sound source in a particular application. For instance, a microphone may have a peak in the 2 – 8 kHz range to increase intelligibility for live vocals.