pH is a major aspect of organic chemistry. Acids or bases promote most organic reactions or are at least involved at some stage in a reaction pathway.
After the needed action is accomplished, pH hyperactivity needs calming down; in a word: neutralized.
Acids and bases are ionic go-getters. It would make sense that neutralizing them has something to do with taking a charge off: deionization (the removal of ions). The ease of neutralization is related to the electronegativity of the elements involved. But something much fatter than electrons easing up is involved. A proton jumps between ions to neutralize. In aqueous neutralization involving an acid and salt, the salt is but a spectator. Proton hops turn acidic ions (H3O+) into water (H2O).
More generally, proton transfer either turns an acidic H3O+ (hydronium) ion into a water molecule or ionizes a water molecule to the base HO– (hydroxide). Transfer takes 1–2 picoseconds, with the proton hopping along a particular pathway.
The local H-bond water network provides a pathway for proton transfer; or not. Without a permissive aqueous dynamic and structure, proton transfer is stymied. A proton may hop its way to a dead end, where it is locally trapped for an extended period.
In a gas reaction, ions clump by attraction. Without any solvent at all, proton transfers neutralize.
Acids and bases mixed in the right proportions neutralize by proton transfer: acids donate protons that bases accept.