Unique to Philadelphia - though perhaps at one time a few may have existed in New York - the trinity house, also known as a bandbox house or Father, Son, and Holy Ghost house, is a small house usually built for the lowest class of servants. Often built for indentured servants or slaves, the trinity house originally contained one room per floor, hence the name.
Completely against William Penn's original intention for Philadelphia to be a "Greene Country Towne", property owners utilized every bit of land they could, particularly when it came to their servants' quarters. Rather than building a rambling shack for their workers, they stacked the space vertically.
Over time blocks were divided and subdivided repeatedly, leaving the main streets such as Walnut or Chestnut for the wealthy home owners, smaller streets such as Juniper and Camac for servants or the lower class, and even smaller streets off those, and sometimes even smaller streets off those, creating a kind of coiled snail shell within each city block.
It is in these smallest of streets (most cities wouldn't even consider them alleys) that we find the courts that held the trinity houses. Usually built facing each other in rows of four, they are all typically the same. Elfreth's Alley contains a great selection of trinities, although these houses are simply very old and predate the development that led to the large scale production of trinities homes as servant quarters and the interior courtyards recently being rediscovered.
Typically these houses would contain three floors, a basement kitchen, and a tiny attic. Each floor would be about 100 square feet, contain a fireplace, and be connected by a pocket staircase tucked behind the chimney. The back would contain a cobbled privy. A very good example of a classic servant trinity can be found in Franklin Court behind Market Street.
Many of the trinities that survive today, many of which can be found in Washington Square and Society Hill, have been modernized and even combined in order to house modern families. Often the privy area and backyards are converted into kitchens or expanded living rooms, some have replaced the pocket staircase with a more convenient staircase, and some have chosen to combine two houses into one. Fishtown, Chinatown, and Northern Liberties still have many examples of well preserved trinities still containing the original layouts which are often used as rentals.