A rowhouse is a long, thin building, always brick, and built one after another, covering an entire block (thus, creating a row of houses). Particularly common in Baltimore, they can also be found in Philadelphia and in some areas in Virginia. They are very similar in style to brownstones, but are hardly ever more than 3 stories high, and made of brick rather than stone. Nonetheless, one could think of rowhouses as being something like a brick brownstone (if you like). Since almost all of my rowhouse experience/knowledge comes from Baltimore, I will admit that the following discussion may not apply fully to other areas.
Like brownstones, rowhouses were built to accommodate
families, especially in the period immediately following the Civil War, and continuing well into the 1920s (most brownstones, I believe, were built before 1900). Since the trend for suburbanization began, rowhouses occupancy began to decline significantly in many areas, and today many (if not most) rowhouses have been split up into multiple apartments. From the outside, they look rather small (being no more than 15 to 18 feet wide), but, I assure you, inside they are huge. A full three floor rowhouse can easily contain 6 bedrooms, 3 bathrooms, a large kitchen and dining room, plus a living room and about a zillion closets.
At this point I would like to extol the virtues of a rowhouse apartment, as compared to a standard issue apartment building. First, the brick walls between your and your neighbors means noise is kept to a minimum (though of course, it will still come through if it's loud enough). Also, the availability of decks, large porches, and sometimes even roof decks makes for a fine time, no matter if you like to have giant parties, or sit alone, watching the stars. Also, the age of these buildings often gives them a lot more personality that an apartment building. And lest I forget, almost all of them have hardwood floors.
That said, there are a few downsides. In particular, the fact that you (usually) have houses directly on both sides of you means little in the way of windows, unless you're in the front or back of the house. This can be partially rectified by skylights, but some rooms will be quite dark even in the middle of the day. Personally, this doesn't bother me too much, as long as the bedrooms have light, but I can see that some people may wish to find another form of housing if this is an issue. If you are extremely lucky and/or rich, you could get one on the corner of a block, which would solve this problem.
Most of the time, you won't get much in the way of a front lawn. Personally, I don't give a damn about this, but I suppose some people might like it. Sometimes you will get enough space to have a few plants or bushes, though in other cases the front stoop will be just a few feet from the sidewalk.
There is a book, The Baltimore Rowhouse, which covers the history of these buildings in great depth.