Keto-enol tautomerism is a reversible equilibrium between a carbonyl (keto) form and its hydroxyl-alkene (enol) form, catalyzed by acid or base. Under normal conditions, the keto form predominates due to greater stability, but the enol form is an important reactive intermediate in many reactions. The mechanism involves protonation of the carbonyl oxygen (or deprotonation of the α-carbon) followed by proton transfer.
From enolate chemistry, you know that the α-hydrogens of a carbonyl compound are acidic because the resulting anion is stabilized by resonance delocalization onto the electronegative oxygen. Keto-enol tautomerism is a closely related phenomenon, but instead of removing the α-proton entirely (to form an enolate anion), the proton simply migrates from the α-carbon to the carbonyl oxygen within the same molecule. The result is an enol — a compound with a hydroxyl group (-OH) attached to a carbon-carbon double bond (an alkene). The keto and enol forms are called tautomers: constitutional isomers that interconvert rapidly through proton transfer.
The mechanism proceeds by two distinct pathways depending on whether the catalyst is acid or base. In acid-catalyzed tautomerism, a proton first adds to the carbonyl oxygen, activating the α-C-H bond. Then the α-hydrogen leaves as a proton, and the electrons from that C-H bond form the new C=C double bond of the enol. In base-catalyzed tautomerism, a base removes the α-hydrogen first, generating an enolate intermediate. The enolate then picks up a proton on oxygen from the solvent, producing the enol. Both pathways are fully reversible, and the system reaches an equilibrium between the two tautomers.
For most simple ketones and aldehydes, the keto form overwhelmingly predominates at equilibrium — typically 99.99% or more. This is because a C=O double bond (in the keto form) is thermodynamically stronger than a C=C double bond plus an O-H bond (in the enol form). However, certain structural features can dramatically shift the equilibrium toward the enol. 1,3-Dicarbonyl compounds like acetylacetone (2,4-pentanedione) exist with a substantial enol population because the enol form is stabilized by an intramolecular hydrogen bond and by extended conjugation across the O-H···O=C system. Phenol is an extreme case: the "enol" form is the aromatic ring itself, and it is so much more stable than the keto form that tautomerization to the keto form essentially does not occur.
Despite its low equilibrium concentration, the enol form is critically important in organic reactivity. Many reactions of carbonyl compounds — α-halogenation, the aldol reaction, racemization at the α-carbon — proceed through the enol (or the closely related enolate) as a reactive intermediate. The enol's carbon-carbon double bond is nucleophilic and can attack electrophiles, a reactivity that the keto form does not possess. Understanding that the enol is always present in small amounts, constantly regenerated by tautomerism, explains why these α-carbon reactions occur at all, even when the enol concentration is vanishingly small at any given instant.