Characteristic impedance (Z0) is the ratio of voltage to current of a wave travelling along a feed line. It is fixed by the line's shape and insulation. It is not loss, it is not a resistance you can measure with an ohmmeter, and it does not change with the line's length.
Where it comes from
Every stretch of line has a little inductance (series) and capacitance (shunt). Their ratio, not any resistance, sets Z0.
Think of the line as a chain of tiny inductors (the magnetic field around each wire) and tiny capacitors (the electric field between the conductors). A wave front must charge each capacitor through each inductor before it moves on, and that fixes the ratio of voltage to current: Z0 = √(L ÷ C). No resistor is involved, so no power is lost to Z0 itself; the energy simply moves on.
Because every stretch of line looks the same, a wave never sees an "end" until it reaches the load. If the load equals Z0, it takes the power and nothing returns. If not, part reflects. See SWR and reflections.
Setting Z0 with geometry
Fatter centre conductor (lower D ÷ d) means lower Z0. More plastic (higher εr) lowers Z0 and slows the wave. Idealised formula.
Z050.1 Ω
For coax, Z0 depends on the ratio of the shield's inside diameter to the centre conductor's, and on the insulator: Z0 ≈ (138 ÷ √εr) × log10(D ÷ d). Because of the logarithm you need big changes in the ratio to move Z0 much. Foam or air lowers εr and raises Z0 for the same size, so a foam cable needs a relatively fatter centre conductor to stay at 50 Ω.
Cross-section (left) sets Z₀. Slide the length: nothing changes.
Z₀ (ideal, air spaced)386 Ω
For two parallel wires it is similar: Z0 ≈ 276 × log10(2s ÷ d) with air between them, where s is the spacing between wire centres and d is the wire diameter. Wide spacing and thin wire give the few hundred ohms of ladder line. The same insulator that sets Z0 also sets the velocity factor.
In practice
Match the line to the gear. Radios, amplifiers and most coax are 50 Ω, so a 50 Ω line makes no mismatch there. Whether the antenna matches is another matter; see SWR and reflections.
A short run of 75 Ω cable in a 50 Ω system gives at worst a modest 1.5:1 mismatch at each end. That is tolerable for short runs, but it is a mismatch.
Kinks, crushing and water change the geometry, so they change Z0 locally and cause small reflections. See Coaxial cable.
Splitting or cascading lines of different Z0 gives a discontinuity at each junction, which is how matching sections work on purpose.