What are "classes" of ships?

I always get confused by this concept. Is it just a style of ship? Do all Galaxy Class ships look the same? Are there other Constitution Class ships besides the original Enterprise? As far as I've seen, there's only one Defiant class, and that's the Defiant, which was replaced by the Sao Paolo which was renamed Defiant, so we are back to one Defiant class ship: The Defiant.

Why have a class for a single ship? Were there other Defiant class ships that we don't see? Did they also have Romulan technology?

It seems like each ship is unique, so why even have classes? The Enterprise-D is entirely different than the next Galaxy class, right?