What do stainless steel, braided brake hoses do?

hey contain the hydraulic pressure to a better degree than stock rubber hoses (thanks to the braiding, they don't expand as much when the brakes are applied). This gives a firmer pedal feel and increased pressure at the brakes, for better stopping.

The braided covering also serves to protect the hose against sharp objects and abrasion.

They typically come in sets of three - two for the front (one for each wheel) and one for the rear (located centrally on a "T" connector).