This can be understood by considering the chemical equation for the reaction:
NaOH + HClO3 -> NaClO3 + H2O
In this reaction, the hydrogen ion (H+) from the acid combines with the hydroxide ion (OH-) from the base to form water (H2O). This leaves the sodium ion (Na+) and the chlorate ion (ClO3-) in solution. Since these ions do not have any acidic or basic properties, the solution is neutral.