A cruise ship is a floating hotel and resort intended to provide an all-in-one package for relaxation and entertainment for its passengers. Cruises can take days or even weeks, with lodging, games, food, and luxuries all provided on board. Many will make stops at various ports along its route to resupply and let passengers off to see the area and get off the ship for a while (by all accounts, lollygaggers will be abandoned if late for departure).
Cruise ships are among the largest ships in the world. The Oasis of the Sea, which was recently completed and will start carrying vacationing passengers on December 1, 2009, is the largest cruise ship in the world, with a length of 1,187 feet (362 meters) and a displacement of over 225,000 tons. For comparison, a Nimitz-class Nuclear Aircraft Carrier is "only" 333 meters long and the largest ocean-going vessel in the world, the TI class supertanker, is just a bit longer at 379 meters. The advantage to such huge ships are simple economics of scale: the more passengers it can hold, the more efficiently it can make money. Larger ships are also able to provide larger and more resource-hungry amenities, which would be more attractive to passengers.
Such massive size means that cruise ships can be fairly independent once they've set out, almost qualifying as a small city. They can carry entire hotels, and multiple purpose-built structures such as casinos, movie theaters, health clubs, tennis courts, nightclubs, and four-star restaurants for its thousands of passengers. They can carry enough fuel to drive them enormous distances across open water (where gas stations are scarce). They're big enough that they stay fairly stable in rough water and bad weather, for passenger comfort. They're so huge, in fact, that their sheer size often limits how many ports they're able to dock with, either due to excessive draft or simply length.
The appeal of a cruise ship is largely that it's a method in which to get away from the stress of civilization without actually leaving any of its luxuries behind, essentially making it an idealized version of city life (plus fresh air and a permanent ocean view) for at least a little while. Furthermore, there are legal advantages to being in international waters, where gambling and duty-free shopping can be indulged. And the staff is committed to each passenger's relaxation and enjoyment, with maid service and meals usually included, and crew members are available to help anyone with disabilities or who might simply be lost on the huge vessels.
In recent years, the reputation of cruise ships has taken a bit of a hit from disease outbreaks. The major disadvantage to being locked in a confined area with thousands of other people is that you're breathing each other's air and rubbing elbows most of the day. This makes it an efficient environment to spread disease, most famously norovirus outbreaks (symptoms include nausea, vomiting, diarrhea, and stomach cramping). A single cruise ship norovirus outbreak can infect hundreds of passengers and there's no way to ensure each one is practicing good preventative hygiene. Fortunately the huge ships have the space and resources for a medical staff, but such an outbreak could easily ruin anyone's planned luxury vacation.
A cruise ship is not to be confused with an ocean liner, which is a similar large, oceangoing vessel. Ocean liners are intended to ferry between two ports primarily for travel purposes, where a cruise ship steams around a smaller loop in gentler waters and is itself intended to be the major vacation attraction. The Titanic was an ocean liner, and its lack of emergency lifeboats and set evacuation procedures lead to the 1912 maritime disaster that it is infamous for. A repeat of this tragic incident would be nearly impossible today given modern safety regulations, largely inspired by such events.
Thanks to The Custodian for some corrections.