Like a persistent cough, you can usually ignore it. Sometimes, though, you shouldn't.
When you flick a light switch, the lights turn on instantaneously because electricity moves at the speed of light, right? Anyone who has taken a basic circuits or physics class knows this isn’t the case—the actual movement of electrons is quite slow. The electromotive force moves quickly, meaning those electrons start and stop moving quickly but even that is not at the speed of light. For a light switch and many low frequency applications, the assumption that these changes occur instantaneously is pretty safe. However, when dealing with RF signals and signal changes are occurring in the nanosecond range, this can become a significant issue.
Propagation delay is the time it takes for a signal to move from one point to another, usually measured in picoseconds per inch. This delay is dependent on the material through which the signal is being propagated, as well as the dielectric surrounding it, but is not related to frequency in any way. So, using the light switch as an example, if we assume a 200 picosecond/inch delay between the switch and the light, 30 feet of wire between switch and light, there will be a 30 feet x 12 inches x 200 picosecond delay, giving a 72 nanosecond delay. While this is based on some assumptions about length and propagation delay of the wire, it gives at least a general timeframe that it takes for the signal to reach the light bulb.
On high frequency boards, it is very common to see traces that seem to zigzag for no apparent reason. This is purely for propagation delay. High frequency signals that move along different trace lengths will reach their destination at different times. If the signal is toggling every couple hundred picoseconds and they arrive at a difference of a couple tens or hundreds of picoseconds, there will be some serious problems. Also, due to the effect of the surrounding dielectric, there are some odd things to remember when doing PCB design. An internal trace, surrounded by FR4 will have a greater delay than an external trace, which is only partially surrounded by FR4 and partially surrounded by air. Air, which has a lower dielectric constant, will have a shorter delay than FR4. So, for practical purposes, if you’re trying to match traces on a PCB, it will be significantly easier to keep all the traces to be matched on the external layer of the board. Of course, requirements may demand you go through the board but then you’ll have some matching challenges with the vias and you simply need to keep it in mind.
I have a PCB focus on propagation delay because that’s more of my area, but propagation delay has a factor in all things RF. If you go into something besides PCB design, you still need to keep this in mind for your waveguides, antennas, probes, and all that fun stuff!