Excelsior Class Starships are the workhorse of the federation Fleet. Designed to fill the gap left by the retirement of the Constitution Class, their hulls incorporated many advantages that left them in service (and still being constructed) after close to a century of regular use.
The prototype of the class (the USS Excelsior, registry NX-2000) was an object of scorn for Scotty - he didn't like the new-fangled technology that went into her engines (more on that in a bit) and he particularly didn't like the idea of her breaking his old heartthrob's speed records. When Admiral Kirk 'borrowed' the Enterprise in an attempt to rescue Spock, Scotty stole the Excelsior's warp control chips as a souvenir. This left the Excelsior dead in space and her new engine designs were scrapped. Whether the one is the direct cause of the other is up for debate.
We've seen Excelsior Class starships in every series from The Next Generation on in varying capacities - they became the standard "meeting with another ship for whatever reason" ship - ferrying admirals around, dropping off new crew members, as part of various armadas (particularly in the massive battle scenes of Deep Space Nine) or wherever else they were needed. The Enterprise-B was an Excelsior Class starship (though that's an interesting oddity - the Enterprise-B as seen in Star Trek: Generations was an Excelsior Class refit, with extra weapon emplacements, more powerful impulse engines and a modified secondary hull. Despite this happening far in the 'past,' every other ship of that class we see, with one exception - the USS Lakota, is of the pre-refit class. Why, I have no idea. I can only assume that there was a problem with the new design - her captain was a bit...er...incompetent, and probably didn't do his ship's namesake justice).
She's a bit difficult to describe, but here goes - they're curvier than their predecessors, with a recessed deflector dish and rounded warp nacelles. The connection plane between the saucer section and the secondary hull is much wider and shorter than the Constitution Class, improving hull rigidity and reducing overall stresses. Likewise, the warp nacelle pylons are boxier and far shorter than the Constitution-class (as well as being connected to the secondary hull in one central place instead of attaching to opposite sides of the hull) while the nacelles themselves are longer and thinner.
The class also features two shuttlebays, one in the traditional Constitution Class placement, the other on the bottom of the engineering section that is usually open to space (the refit has a third shuttlebay directly under the first, making her a truly awesome mobile fighter platform even if we've never seen them used that way).
Weapons and Armament
Weapons emplacements are nearly identical to the Constitution Class, though the ship's newer powerplant allows for far more raw output than her predecessor. Rear-facing phaser turrets help eliminate the Constitution Class' sizable rear-angle blind spot, but not by much - the ship still has only two photon torpedo tubes, both forward-facing - if she doesn't go into a conflict head-on, she's at a serious disadvantage (as opposed to the later Ambassador and Galaxy Class starships that were essentially huge, multidirectional weapons platforms if they needed to be).
Power Plant (or: 'Let's do the Transwarp, agaaaaaain')
Initially, the Excelsior prototype was designed as the test-bed for a new warp theory implementation. Called the Transwarp Drive, it was supposed to make the ship's warp engines more efficient. The program was scrapped after the NX-2000's rather spectacular failure at the hands of Mr. Scott, but her spaceframe was considered to be more than acceptable as a Constitution Class replacement. Refitted with standard engines, the Excelsior Class proved to be the hardiest starship design in Starfleet, weathering normal wear and tear far better than her predecessor.
I should also note that this class is one of the most cannibalized in all of trek history - if you see some random ship floating by in the background, dead or dying, it's probably a wrecked Excelsior Class model with some bits switched around.