Most antennas are designed to have an impedance of 50 ohms.

If the vertical radiating element is 1/4 wavelength and the radials are 1/4 wavelength or you have a solid ground plane with a radius of around 1/4 wavelength or longer then the impedance will be close to 50 ohms.

If you make the radiating element 5/8 wavelength the antenna will have slightly higher gain but capacitive reactance increases the impedance to something like 1000 ohms if I remember correctly.

You need some type of matching circuit that changes the impedance back to 50 ohms. Adding a coil (inductor) adds inductive reactance which cancels out the capacitive reactance.

Here are some pages with links to antenna theory web sites

Antenna - Antennas: Theory
Amateur Radio Antenna Projects