aldehyde oxidation
Aldehydes sit on a knife edge between alcohols and acids, and they are easily nudged the rest of the way: oxidation turns an aldehyde (R-CHO) into a carboxylic acid (R-COOH). This is so easy that aldehydes slowly oxidize in air on their own, which is why a bottle of old aldehyde often contains some acid.
The reason aldehydes oxidize while ketones generally do not comes down to one hydrogen. Oxidation here means removing the hydrogen attached to the carbonyl carbon and adding an oxygen-containing group; an aldehyde has that lone C-H to lose, but a ketone's carbonyl carbon is bonded only to other carbons, with no such hydrogen to remove, so it resists mild oxidation. A wide range of oxidants do the job, from strong ones like potassium permanganate (KMnO4) and chromic acid to milder, more selective reagents.
Because this difference is so clean, it powers classic diagnostic tests. Tollens' reagent (a silver-ammonia complex) oxidizes an aldehyde and is itself reduced, depositing metallic silver as a shiny mirror on the glass, a positive test ketones do not give. Fehling's and Benedict's solutions do the analogous thing with copper, forming a brick-red precipitate, and are used to detect reducing sugars (which exist partly as open-chain aldehydes). So a simple oxidation becomes a color-changing window into chemistry.
Adding an aldehyde to Tollens' reagent and warming gives a brilliant silver mirror on the inside of the test tube; a ketone leaves the tube clear, distinguishing the two at a glance.
Aldehyde plus Tollens' reagent: a silver mirror forms; ketones give no reaction.
The catch-all 'ketones cannot be oxidized' is a simplification: ketones do resist mild oxidants, but very harsh conditions can cleave them at the carbonyl by breaking C-C bonds. For ordinary lab and test purposes, though, only aldehydes give the easy oxidation.