acid-catalyzed hydration
Acid-catalyzed hydration is the addition of water across a double bond to make an alcohol, with a strong acid (typically dilute sulfuric acid) doing the catalysis. The net change is simple: an alkene plus H2O becomes an alcohol, with H going to one carbon and OH to the other. Because water alone is far too weak to attack a placid pi bond, the acid is essential — it provides the proton that gets the whole electrophilic addition started.
The mechanism is electrophilic addition with water as the nucleophile. First a proton from the acid adds to the alkene to make the more stable carbocation (Markovnikov). Then a water molecule, using a lone pair, bonds to that positive carbon, giving a protonated alcohol (an oxonium ion). Finally that extra proton is handed back to the solution, regenerating the catalyst and leaving a neutral alcohol. Every proton consumed is returned, which is exactly what 'catalytic' means.
Two honest caveats make this reaction less used in the lab than it looks. First, it follows Markovnikov, so it gives the more-substituted alcohol — useless if you want the other one. Second, the carbocation intermediate can rearrange, scrambling the product. For these reasons chemists often prefer oxymercuration (Markovnikov, no rearrangement) or hydroboration-oxidation (anti-Markovnikov) when they need a specific alcohol; acid-catalyzed hydration shines mainly in bulk industrial processes where the alkene is symmetric or the issue does not arise.
Propene plus water with dilute H2SO4 gives propan-2-ol (CH3-CHOH-CH3), the Markovnikov alcohol, because the proton adds to make the secondary carbocation rather than a primary one.
Water adds Markovnikov; the acid is regenerated, so it is a true catalyst.
Hydration and its reverse, acid-catalyzed dehydration of alcohols, are the same equilibrium run in opposite directions; you push toward the alcohol with excess water and dilute acid, and toward the alkene with concentrated acid and heat that removes water.