Under normal string tension, the guitar neck should have a slight concave curvature. By creating a counteracting force, the truss rod prevents the neck from bending excessively under the stress placed on it by the strings.
The necessity of a curvature is very important.
As a string is plucked it vibrates from side to side and also up and down.The string moves in a rotary oscillating motion. A string that is fixed at both ends (nut and bridge) moves mostly at its centre where the least amount of tension is. String relief is required to allow the string to vibrate freely.