Long story short, the strings need to be able to pass without binding over the nut (and to a lesser extent, the saddle and tuning posts). Otherwise, the pitch will not respond smoothly whenever you tune, bend, or operate the "tremolo"/vibrato/whammy bar. This neat little kit provides a good solution.
The problem is ameliorated by the use of a nut made of a low friction material such as buffed bone and by the choice of a headstock setting the tuning pegs inline with the strings. Even so, your setup will still benefit from a tiny smear of lube in just the right spot. With a cheap plastic nut, or strings that don't pass straight over the nut, your guitar setup will benefit even more so.
The grease is thick enough that it stays in place over time and thin enough that it can be applied without fuss at room temperature. The supplied applicators are useful.
The tube comes only half full, but since you only need to apply the tiniest amount, it may well last a lifetime unless you're a full time luthier.
Although I haven't tried it yet, I daresay this grease would also be suitable for the sliding surfaces of tuning machines and trem mechanisms.
I'd recommend it for all steel-strung fretted instruments, electric or acoustic.