First, a couple of
clarifications of the above writeups. Neither the center conductor or the braid/shield carry the
signal. The signal is carried via electromagnetic waves that
propagate inside of and down the cable. The center conductor and shield form a circular
waveguide through which various modes may be excited through the introduction of RF frequency voltages at either end.
Back in the old days of radio transmission, parallel-conductor transmission lines such as ladder line were commonly used to connect the transmitter to the antenna. Parallel-conductor lines are great because they are inherently balanced and their intrinsic impedance at RF often matches that of the antenna being driven.
The electromagnetic modes on a parallel-conductor line unfortunately results in field lines extending into space around the two conductors. This is bad, because this causes the line to immediately couple to any conducting objects nearby. These feed lines are not good to feed a vehicle-mounted antenna, for example. Running this feed line up the side of a metal tower couples with the tower itself, changing the impedance of the feed line. This acts to lower the overall efficiency of the transmitting system (and drive up the SWR due to impedance mismatches, which can blow up your radio unless you have an antenna tuner). Parallel feed line also needs to remain parallel and straight, which reduces your ability to fold, bend, or otherwise shape it to fit the environment.
Coaxial Cable was invented to solve this problem. Coax is an electromagnetic waveguide just like parallel-conductor line. All the fields, however, exist between a center conductor and the outer conductor (the braid or shield, depending on whether it's braided outer-conductor line such as RG-6 and RG-8, or hardline such as Heliax). No fields exist outside the cable (theoretically, anyway). This is awesome because you can immediately attach it to anything metal and it won't couple to it. You can use it inside vehicles, tape it to the side of your house or your transmitting tower and it won't appreciably change its impedance. You can also put bends into the cable, so you can run it around corners, make loops out of it, and so on, with almost no RF side-effects.
The down-side of coaxial cable is that it's lossy. The dielectric material that fills coax cables isn't perfect. This is why it's important to buy high-quality coaxial cable when you need to reduce energy loss at RF frequencies.
Dispersion
It is *very* important to remember that the electric properities of the dielectric inside the cable are not frequency independent. The permittivity and permeability of dielectric materials actually exhibit quite a bit of frequency dependence over wide bandwidths.
Why is this important? Consider the propagation speed of a wave on the line. This speed is dependent on the frequency of the wave, and the properties of the dielectric, which are frequency dependent. What does this mean? A signal with a very wide bandwidth has frequency components that travel at different speeds along the cable. The result? The waveform you get out is not the same as the waveform you put in. If you have a crappy cable, this distortion may be more than you can tolerate.