The Star Trek universe's Constellation class starship was designed with a very specific purpose in mind - it was built from the ground up as a deep space exploratory cruiser.
This class' inception and history are a little hazy, but certain things can be inferred by the design of the ship itself. Judging from the hull configuration and, more importantly, the designs of the warp nacelles, it can be inferred that her spaceframe dates from the movie years - the dorsal surface of the primary hull looks like it was taken from the Constitution Class refits, and the engines look to be borrowed from the Miranda class and their ilk, as does their bridge. It's probable that they were kept in service because they were so well suited for what they were designed to do that their replacement wasn't considered necessary until their exploratory and diplomatic roles were taken over by the Galaxy class.
She's definitely an odd one. The primary hull is squared at the back, much like the Miranda Class (although the shuttle bays are located on the sides of the saucer instead of the back). The saucer itself is much thicker than normal, essentially tripling internal volume while only doubling the mass. She's got a bite as well, with outboard weapon and sensor pods mounted along the bottom of the primary hull. The impulse drive is mounted vertically in between the tandem warp nacelles.
Which brings us to her engines. Since she was designed to operate outside the bounds of federation space for years at a time, it was deemed critical that ships of this class should have extra safeguards against becoming stranded. To this end, (and also because of the ship's higher than normal mass) the ship is fitted with four warp nacelles instead of the usual starfleet standard of two. This, supposedly, allows for better fuel efficiency and longer cruise durations while allowing her to limp home at low warp on two nacelles if critically damaged.
Captain Jean-Luc Picard's command before the Enterprise-D was the USS Stargazer, a Constellation Class starship (as seen in the Next Generation episode "The Battle.") Originally, the show's production crew intended to reuse the movie era Constitution Class model but changed their minds when they realized how long the class would have been in service by Picard's time. (Sidenote: as far as I know, we NEVER see a constitution class starship in service on Next Gen, DS9 or Voyager.) This change was made after the episode was filmed - at one point, Levar Burton says "Constitution Class" but has "Constellation Class" dubbed over the line - to facilitate that, a class name needed to be chosen that was similar enough to the original so as not to look completely loopy on screen.