Coaxial cable ("coax") is a centre conductor wrapped in an insulator, then a tubular shield, then a jacket. It is the default feed line in amateur radio because it is self-contained: you can run it along a mast, bury it, or lay it next to metal without disturbing the antenna.
How it works
A working coax keeps its fields inside. Current on the inside of the shield is a mirror image of the centre conductor's.
The signal travels in the insulator between the centre conductor and the shield. The current on the centre conductor is matched by an equal and opposite current on the inside surface of the shield, so their fields cancel outside the cable. At radio frequencies, current crowds onto surfaces (skin effect), so the inside of the shield carries the signal while the outside is a separate conductor. That detail matters later: if current ever flows on the outside, the cable itself radiates and picks up noise. See Common-mode chokes.
Thicker cable has lower loss, but it is heavier, stiffer and costs more. Foam insulation lowers loss further. The usual families, from thin to thick:
Class
Typical use
Trade-off
Thin (RG-174 type)
short jumpers, handhelds, QRP
flexible but lossy
RG-58 type
short HF runs, portable work
cheap and light; loss grows quickly on VHF and UHF
RG-8X type
medium runs, mobile
a middle path
RG-213 / RG-8 type
HF and VHF base stations
thick, low loss, solid and stiff
Foam low-loss ("LMR-400 class")
long VHF and UHF runs
low loss for its size; stiffer, wants matching connectors
Hardline
repeater sites, very long runs
lowest loss; rigid or semi-rigid, costly, special connectors
Pick by frequency and length: on HF, 100 feet of RG-8X is usually fine; on 70 cm the same run can swallow most of your power. See Feed line loss and velocity factor for the numbers.
Foam is mostly air, so it loses less per foot. Water in the cable is what kills it.
Why 50 Ω? For air-filled coax, loss is lowest near 77 Ω and power handling is best near 30 Ω; 50 Ω is the compromise that became the standard.
In practice
Don't kink it or crush it. A sharp bend changes the spacing between conductors, which disturbs the impedance and can damage the dielectric.
Seal outdoor connectors. Water that enters a cut end or an open connector wicks along the cable and ruins it, and foam cable is especially vulnerable.
Use cable rated for UV and outdoor use, or protect it, because jackets crack in sunlight over years.
75 Ω cable works in a pinch for short runs on HF, but it is not a match for 50 Ω gear. See SWR and reflections.