Livery means "a servant's uniform" and in Downton Abbey refers to the distinctive tails the footmen wear. Since footmen work in the upstairs rooms serving the noble family, their elegant appearance is considered a reflection of status and pride of the family itself.
As you might expect, livery is related to deliver and delivery and comes from the Medieval French word meaning "delivery." In English it originally meant "apportioning of provisions especially to servants" or "allowance." Over time, it came to refer to the distinctive clothing of servants: the term livery color referred to the color of the clothes issued to servants by feudal lords. Livery can also mean the act of delivering legal possession of property and the care and housing of horses for pay.
And a livery stable is where horses and vehicles are kept for hire, which led to the term's use for the registration of taxicabs.
