The Nebula Class Starship was premiered in the Star Trek: The Next Generation episode The Wounded, and was the first new ship design shown that was an obvious descendant (from the model builder's perspective) of the Galaxy Class. Featuring a compact, vaguely insect-like design, the class features design elements borrowed from the Miranda Class and her various retrofittings while maintaining the fluid lines of 24th century spaceframe engineering. Designed as a slightly less capable sister to the Galaxy Class, Nebula Class Starships are extremely customizable, heavily armed and nimble.
The Nebula Class was designed concurrently with the Galaxy class using similar spaceframe components. It is postulated that the Nebula Class was initially designed in response to escallating tensions on the Cardassian border. This turned out to be a wise move, as ships of this class saw heavy action in the Cardassian War, circa 2350.
Ships of this class have been seen in various episodes of the Next Generation, of Deep Space 9 and, occasionally, of Voyager.
Much like the Miranda Class, Nebula Class starships feature underslung warp nacelles that sit almost directly beneath the ship's saucer (a saucer that is, incidentally, identical to that of the Galaxy Class with the exception of the elimination of Galaxy's secondary impulse engines). The nacelles are mounted in a novel (for the time) configuration, hanging down from a N-shaped bar that is mounted to the top of the secondary hull. Also like Miranda, ships of this class have a sensor pod that sits on its back. Unlike Miranda, that pod is swappable and can contain anything from advanced sensor suites to heavy weapons emplacements to extra warp nacelles - since the ship was designed as a short to medium range interdiction/escort vessel, this allows the ship to be quickly configured for a variety of mission assignments without having to carry all the necessary equiptment with it wherever it goes. This reduces extended mission flexibility but improves resource management for shorter assignments. This is an odd idea considering that ships of this class fulfill exploratory roles during peacetime, lightyears from friendly starbases.
Also unlike Miranda, this class has a true secondary hull and full deflector suite nestled between the warp nacelles. A connection plane between the saucer and engineering section is noticably absent, compressing the ships' component parts into an extremely compact form. This has its advantages - a tight configuration of this sort reduces target profile from the z and y axes, making it harder to hit than its swan-like sister - the Galaxy Class, pretty as she is, is almost impossible to miss from below.
A ship of this size is almost certain to carry families aboard as part of its peace-time operations, but the hull configuration makes saucer separation impossible. Hopefully there are other ways of saving the civilians in the event of an emergency (or I'm totally wrong about the families - it happens), but that has never been seen.
Assuming her powerplant is identical to Galaxy's (and there's no reason NOT to assume that), Nebula Class Starships pack a mean punch - with a minimum of five phaser arrays and one fore-facing photon torpedo launcher along with the possible weapon capabilities of the mission configurable pod, these ships are capable of waging a war all by themselves (which is precisely what Ben Maxwell used a Nebula Class starship for in the episode featuring the class' appearance). Taking into consideration the edge in maneuverability it has over the Galaxy class due to its slightly reduced mass, this ship was a clear contender for 'most badass non-unique starship ever' until the Defiant class came about and made this baby look like an adolescent with a bb gun.
There are some doubts as to whether this class predates the Galaxy Class or comes after it - the drive to go with the latter is strong, as we're only introduced to it in TNG's fourth season. Nevertheless, evidence seems to be on the side of the former. Personally (and coming from a guy who just wrote up something that doesn't technically exist) I don't think it matters all that much.