Oh, gallant was our galley from her carven steering-wheel
To her figurehead of silver and her beak of hammered steel.
The leg-bar chafed the ankle and we gasped for cooler air,
But no galley on the waters with our galley could compare!(from) The Galley Slave, Rudyard Kipling
Basic Information
The War galley was a specific type of warship, mostly indigenous to the Mediterranean which was primarily designed to attack with a ram.
Since the primary purpose of these ships was to run headlong into their target at the fastest speed possible, their whole design philosophy revolved around going fast in a straight line. The resulting ships were long, thin and oar powered, sacrificing pretty much all other design features for specialisation in ramming - a few marines might be carried to engage the enemy once the ram had occured, but (initially at least) little else in the way of weaponry.
The galley design is very old - stretching back into classical antiquity and surviving into the late 19th century when the age of steam put an end to them. Over time the basic design varied quite a bit and some true freaks of engineering appeared from time to time including the late Hellenistic "Sixteeners"1 and size did increase a little over time (although after the Hellenistic giants things did settle down a litte) allowing the transition from "mainly ramming" to some use of ordnance. By the nineteenth century galleys were well known for mounting a small number of (often fairly large) guns which could fire straight ahead (something which which contemporary sailing ships struggled) and, by use of the oars, being able to turn and manouver independant of the wind (ditto).
Wind independant propulsion, at a (somewhat) discretionary speed - which could (for a brief period at least) be quite fast - was the galley's main strength. It's weakness was the fact that it required an enormous crew. Obviously, manpower is always an issue - and as a function of manpower, the ships also had a high requirement for food and - more crucially water. Since galleys were designed to be fast they had nothing like the amount of space required to carry crew stores for more than a few days and so had a very limited operational radius. Also, whilst almost all galley designs carried at least a single sailing mast, the fact that they relied on a falliable human crew for most of their propulsion was another significant weakness - once the oarsmen were exhausted, they were exhausted - the wind can blow all day if it feels like it.
Also, despite portrayals to the contrary, most galley oarsmen historically were not slaves or convicts but free men (albiet often of pretty low status) and - in some cases - soldiers who effectively rowed themselves to their target, defeated any local opposition in a naval battle and then landed to continue the campaign on land … or not. There were periods when forced rowing was common (notably the early modern period) but in general, a shipful of hostile oarsmen was something of a liability in combat. The design of the rowing positions appears also to have had a significant bearing on the requirements for crew quality - early classical Greek designs with single rowed oars required a highly skilled crew, which was hard to achieve with forced labour, whilst with multiple men at each oar, only the one at the handle end needed to be relatively well trained (mainly so that the stroke could be kept up without the oars fouling one another).
Besides range issues, the traditional light, stiff hulled build of most galleys (again, for speed) made them fail to thrive in rougher seas where they tended to suffer badly from wave damage in normal operation - although they were frequently used for costal work in the summer months, use was much less frequent. The Scandinavian Dragon ship has some resemblance to early galleys such as the pentekonter, albiet with modifications for the rough seas of the North, and seems to have operated in much the same way.