A townhouse describes a single family home in a row of houses that share a side wall. Usually they are up to 4 stories high with no elevator. They were built at the end of the 19th century as single family homes.
When a neighbourhood became unfashionable the owners often moved out and turned the stories into apartments. These apartments usually feature small bedrooms and the buildings do not have elevators. Generally they have high ceilings and sometimes fireplaces and exposed brick walls.
As you can see in the image to the right, even the 1st floor has a stoop, which you will have to climb.
In New York a lot of townhouses were built with brownstone, which is a brown Triassic sandstone, and are therefore often called 'Brownstone'.
You will love the charm of these apartments, but if you are in any way handicapped, they are not for you!