A radio's antenna both receives radio waves in and transmits radio waves out. When transmitting, it is important to have the antenna's impedance matched to the radio outputput impedence, which is typically 50Ω. A mismatch causes power to be reflected back into the transmitter which can turn into heat and destroy the amplifier circuit of your radio. The SWR, or "Standing Wave Ratio", is a measurement of how well the antenna is matched to the radio and a perfect match is 1:1.
There are many types of antennas, and they have different purposes. An antenna that lets you talk to radio operators in Europe might not let you talk to someone in the next town over, and vice versa. Here's some basic types of antennas and their pros and cons:
Dipole: Perhaps the simplest antenna is the dipole. It consists of two wires run horizontally in opposite directions. Each of these wires should be cut to a length that is a 1/4 of the wavelength on wish you wish to transmit. The dipole is (mostly) a single band antenna.
Dipoles should be generally raised at least a half wave above the ground for long distance communication. This will allow the signal to be emitted at a low angle and the waves will bounce off the ionosphere landing hundreds or thousands of miles away, allowing you to communicate great distances. However, having a dipole closer to the ground will cause the signal to go almost straight up and the rays reflected off the ionosphere will land relatively close to the transmitting radio, allowing you to converse with people close to home. This is called NVIS for "Near Vertical Incidence Skyward".
Doublet: A doublet antenna is almost the same as a dipole, with two wires running off in opposite directions, except that rather than coax going from the radio to the feed point, there is a pair of parallel wires, seperated by insulating material such as plastic. This parallel feed line can be 75Ω "ladder" or "window" line, or 300Ω twinlead, or two wires seperated by insulating sticks.
Off Center Fed Dipole (OCFD):
1/4 Wave Vertical :
End Fed Half Wave (EFHW):
Random Wire: