Warcries are a varied skill tree in the Barbarian's arsenal. There is a lot of variety in this tree indeed, ranging from attack skills to aura-like bonuses to corpse skills. There are actually seven Warcries in the skill tree, the other three are corpse skills, grouped in here by default.
Warcries are cast with a right click, and are a sort of spell. When casting them the Barbarian throws his arms up and his head back and howls. The warcry is shown as a nova of brightly-colored light moving out from the Barbarian in an expanding ring. All warcries have a distinctive graphic, but the sound the Barbarian makes is a random one each time. The Warcries all have different ranges, with the beneficial aura-like ones generally going nearly full screen, while the attack Warcries that hurt monsters have much less range, usually just a few yards.
With beneficial Warcries, other characters and minions must be in range of the Warcry (basically anywhere on the screen is close enough) when it is cast. They'll then enjoy the benefit for the duration of the skill, which depends on how many points the Barbarian has in it. Beneficial Warcries should be refreshed before they expire. Battle Orders especially, since it adds to the maximum potential hit points and mana, and must be filled up with leech or potions.
The three corpse skills are very useful as well. Find Item is one of the most powerful skills in the game, in terms of finding good equipment, and Find Potion can be very helpful also, for the more patient Barbarian. Grim Ward is one of the neatest skills in the game in concept and appearance, but it's hardly needed or used in the game, since the Barbarian is so powerful in other areas.