I Googled this, but didn't find anything that could put it in layman's terms for me to understand. I know it has to do with signals/ pulse compression, but I am not grasping what exactly it is. If anyone could help, it would be appreciated.
(Digging out some OLD memories here...)
Imagine, for the sake of argument, a 5 millisecond radar pulse. By itself, that pulse gives you a certain amount of error in your range estimate.
Now divide that pulse into several shorter "chips", and reverse the phase on some of the chips, and leave the others alone. When the pulse bounces back at you, the phase reversals will still be discernible. Signal processing can figure out very closely, using correlation math, how much the pulse was delayed, and give you a significantly more precise (and accurate) range estimate than you could get from the plain vanilla pulse
The tricky part is picking the chips to phase-reverse. That's what the Barker codes are: they tell you how many chips to use, and which ones to reverse. I know nothing about the math used to develop them. An OLD memory says that the longest-known code is 17 chips, but the commenter says the longest-known is 13, and on reflection I think that's correct.
The effect is about the same is compressing the pulse, making it a lot shorter in time. Normally, this would require a much more powerful transmitter, and a much faster pulse switch on the transmitter.
If you modulate a pulse with a Barker code it will have a high autocorrelation for zero offset but very low autocorrelation for other offsets. In other words the signal is hard to mistake for itself with a time offset. This means if you are trying to detect a pulse or signal you can detect it very accurately in time. This is especially good for radars. It also means that the spectrum of the signal is very flat, i.e. it has equal power everywhere in its frequency range.