What it is: The nut is one of the smallest and most overlooked component of a guitar but it’s also one of the most important. And it’s also where the “conservative approach” of a factory setup is evident.
What it does: The nut is in charge of giving our strings the right spacing and also of setting the action on the first frets. There is a night and day difference between a nut with shallow slots and a nut with well-cut slots. The former not only will bring a poor playability at the first frets (i.e. the strings will be too high) but will also be one of the main culprit of an incorrect intonation. Open chords will sound out of tune. Last but not least, it’s one of the main responsible of poor tuning stability (“G string syndrome” on Gibson guitars, anybody?), no matter how fancy your new locking tuners are.
DIY Tip: Graphite, Vaseline, Big Bends are all great products but they can nothing if the slots are poorly cut. A too narrow or irregular slot will trap your string at every bending or, even worse, if you use a tremolo bridge, impeding the string to go back in its zero-position. I would not recommend the task of filing the slots to everyone as it requires a meticulous approach, proper files and it doesn’t have a way back: if the slot has been cut too deep, the related open string will buzz on the first fret.
Wrapping it up: a good nut has slots cut with the correct depth, width, regular edges and, just eventually, lubed.