The Gunboat is a very fast, one-masted military ship with a small cargo hold. It is armed with a front howitzer, though not the sturdiest.
Its only variant is the Pirate Gunboat.
The first military ship that can be built, the Gunboat seems unimpressive at first pass, being also the most fragile ship on the water. Looks can be deceiving, however. The Gunboat is the only sailing ship that can fire directly forward, which combined with its speed makes it the best ship in the game for pursuit. Gunboats can wreak havoc on trade routes since they can overhaul any ship excepting a full-speed Clipper, racking up huge financial damage even if they wind up being sunk in the process.
Pirates love fielding swarms of Gunboats, to strike unescorted trade ships or swarm down lone warships sent to fight them. A real military will demand at least the use of Frigates--Gunboats will never take a harbor--but any enemy can make use of these small but keen ships to make a busy opponent's life hell.
While any ship with a gun on it is technically a gunboat, in the pre-steam era the term referred to exactly what is depicted in Anno 1800: a small, single-decked ship with a single gun forward (and maybe one aft). Easy and cheap to build, these ships were excellent for coastal defense or use on inland seas such as the Baltic Sea.
Small ships such as this would give their name to the term "gunboat diplomacy", as even a small warship could bully a country with no warships. Variations on the concept would survive all the way into World War 2--the sinking of the US gunboat Panay would almost start a war with the Empire of Japan in 1937.
Game Update 5 (September 10, 2019):