The War Barge is the most basic unit available to non-Western factions (excluding Turkey), and is best described as a simple oar-powered warship that fires arrows. It's comparable to a Galley with the sole exception being that the War Barge carries far less armour in comparison, and also doesn't have the same amount of firepower as well (compared to the Galley which carries a slow but powerful cannon). Additionally, the limited strength of the War Barge's weapons means that it cannot do much damage to buildings, nor can it be used to destroy the more powerful fortifications of many factions, so you should take this into account when constructing your navy.
Unless you have no choice (like you are using a faction such as the Lakota or the Iroquois) you are better off constructing other units where possible. In any case, the War Barge is a very useful unit that can be used in fending off attacks by buildings such as Castles and Towers in order to facilitate an amphibious landing.
In Swords of the Prophets, the War Barge is treated not as a siege vessel, but as a "medium ship" - in other words, it replaces the much cheaper and weaker Dromond and Karve, but this means that for factions which use it instead of the cheaper Dromond or faster Barque, they often find themselves unable to truly master naval combat.