Having a straight guitar neck is important not only for the health of the instrument, it is also important for playability. Either having relief or back bow in the neck will create action problems that will lead to string buzzing or intonation issues. The neck must also be straight when you are doing repairs on your guitar's frets. If you level the frets with relief in the neck, the low and high frets will be sanded down more than the middle frets will. The easiest way to tell if your neck is straight is to look down the side of the fretboard and eyeball it. Sometimes you need your guitar neck to be more accurately straight than just eyeballing it. That is where the notched straight edge comes into play.
In order to truly tell whether your guitar neck is straight, you will need to use a straight edge. A straight edge is a metal ruler that is precision ground on one or both edges to give a perfectly flat/ straight edge. Ordinarily you could just use a straight edge to check whether something was flat or not, but your guitar fretboard has frets inlayed in it. A regular straight edge would just sit on top of the fret. It wouldn't give you a true measurement of how straight your neck is. A notched straight edge is a straight with notches where the frets are on the fretboard. This way the straight edge can touch the fretboard without touching the frets.
Now that you know what a notched straight edge is, you can check the straightness of your neck. Simply take the straight edge and place it against the middle of your fretboard. Shine a light behind the straight edge. If you see light passing through between the fretboard and the straight, it's not quite straight. You will need to adjust your truss rod.
Until you develop your eye, you will definitely need a notched straight edge in your guitar repair bench. You will need it even if you can spot a crooked neck a mile away. It's a good luthier tool to have. If you would like more information about how to use a notched straight edge and straighten your guitar neck, please see my how to adjust truss rod article.