How does cooking oil hide or restore wood furniture?

The oil hydrates the wood and makes it appear darker which usually helps it blend it with the hydrated look that the finish gives the wood.

Cooking oil is for cooking. Try some WD40 or find a made for wood product.

I wouldn't use cooking oil on furniture, it can get rancid. Stick to furniture wax and if you want to cover scratches, try Old English furniture scratch cover.

oil on wood better than wax http://www.woodworkersjournal.com/understanding-oil-wax-finishes/ Fixing Scrapes and scratches:

--Scratches can easily be treated with touch-up sticks. They come in numerous colors and shades and are available at paint shops & Amazon

--Hide scratches on mahogany or dark cherry by rubbing them with a cotton swab dipped in iodine. For unshellacked maple and cherry, dilute the iodine by 50% with denatured alcohol. To darken a scratch, rub it gently with the meat of a walnut. Rub the kernel of the nut directly into the scratch, not into the surrounding wood.

--For scratches in oil finishes, rub with fine steel wool and lightweight mineral oil or boiled linseed oil. Let the oil soak in, then wipe dry.

--Remove light burns with a thin paste made by mixing rottenstone or finely powdered pumice (available from woodworking suppliers) with linseed oil. Rub the paste in the direction of the grain with a soft cloth. Continue until the burn disappears.