The xebec owes much of its design to the earlier galleys and galleasses of the Mediterranean. The root of the name probably comes from an Arabic word for 'small ship', and is rendered into English in three forms: 'xebec', 'chebec', and 'zebec', though the word exists in many other languages as well, indicating its popularity (or at least knowledge of its existence) in the rest of Europe.
These ships had long narrow hulls, and were fitted with oars like their galley predecessors. They were intended to be fast and maneuverable, whether under oar-power or under sail.
17th and 18th century Christian shipping in the Mediterranean was threatened by the Barbary corsairs, who were Muslim pirates based in Northern Africa. The vessel of choice for these pirates in the early days was the galley, whose oars allowed them to overtake merchant vessels caught in light wind. But as time wore on, the trading nations responded to the threat by deploying warships to tackle the corsair problem. Galleys were swift and carried many men, but were not designed to stand up to the broadsides of modern warships.
In response, the Barbary Corsairs evolved their galleys into a new design that would stay competitive with the warships sent against them. In order to mount broadside guns, they widened the hull for extra deck-room and stability, and they removed many or all of the rowers to make room for broadside guns. These changes shifted the motive power of the vessel away from oar-power and onto the three huge lateen sails. And thus, the graceful and distinctive form of the xebec was born.
Their foremasts are typically raked forward, while the main and mizzen were either straight or raked slightly back. The massive lateen yards were so large that they were frequently composed of two spars lashed together -- more like masts than typical yards. Most xebecs did not have a bowsprit, but their beakheads frequently featured a long prow.
A few of the western nations tried square sails on the xebec's mainmast and sometimes even the mizzenmast. The square-rigged mainmast would have topsails and even topgallants, and the mizzen would have a square topsail (while still maintaining the lateen lower-sail). A xebec rigged this way was known as a Polacre-Xebec.
Commonly, though, the standard lateen rig for xebecs had a single triangular sail on each mast, and had none of a square rig's topsails or topgallants. The lateen rig offered many advantages over the square rig, the most significant of which was the ability to pinch far closer to the wind than square sails could. This meant they could both quickly catch up to and quickly flee from square-rigged vessels when sailing close to the wind.
The corsairs favored the xebec for its speed and maneuverability, and for its shallow draft which also aided in escaping larger vessels. These qualities were recognized by many of the European navies, and the vessel was quickly adopted into the Mediterranean squadrons as commerce-raiders and anti-piracy cruisers. As warships, xebecs mounted as many as 36 guns on their topdeck. Depending on the weight of the guns, this made them competitive with naval sloops of war, and even with some of the frigates of the day.
The xebec under sail was a beautiful sight, and it is said that the design was one of the fastest and most agile in the Mediterranean. Some of the same qualities that made it so successful in light seas also made it unsuitable for rough weather. The low freeboard and the shallow draught made the vessel vulnerable to swamping, and it would roll heavily on anything more than moderate waves. Thus, the advantages that the xebec has inland make it a poor choice for open-ocean sailing.
Xebecs were also lightly-built vessels. Unlike the massive, bulky timbers of ships of the line, xebecs were delicate and graceful. They were gazelles, not war-horses. Their tactics in battle reflected this. Xebec captains were loath to engage a foe of equal armament in a gun-battle. Instead, they relied upon their speed, maneuverability, and sweeps to pick their battles, and deposit large numbers of boarders on the decks of their enemies.
The xebec's qualities of speed and shallow draught, and the ability to sail extremely close to the wind, are highly prized by traders as well -- particularly those engaged in the coastal trade and its close cousin, smuggling. While it requires a somewhat larger crew, and has a smaller cargo capacity than other vessels of similar size, its sailing characteristics and combat ability make it an excellent choice for those interested in a swift and powerful coastal vessel.
Historically, the xebec was not well-represented in the Caribbean. It wouldn't have easily made the crossing from Europe, for one thing. A xebec captain risked outright sinking in rough seas and bad weather, far from the somewhat calmer waters of the Mediterranean that the ship was designed for.