Leaders can arise when an elite unit wins a battle. The leader may be used either to create an Army or to hurry production in a city, even a Small Wonder or Great Wonder. When the leader does either of these things it disappears.
The Heroic Epic increases the chances of Leaders appearing from battle.
In the Conquests expansion, leaders are split into Military Leaders and Scientific Leaders. Military Leaders appear as a result of battle as described previously, while Scientific Leaders appear as a result of a civilization being the first to research a scientific breakthrough; civilizations with the Scientific strength have a higher chance to have these leaders appear. Scientific Leaders cannot build an Army, but can be used to start an Age of Science, however this feature is broken in all versions of civilization 3. As such it would be a waste of the unit, it would be better instead to rush a Great Wonder.
Throughout history special individuals have come to prominence on the world stage. Each embodied in some way the ideals and dreams of their people, causing legions to follow their lead. These great leaders of mankind were capable of feats that created benefits well beyond what they could achieve by themselves. On the battlefield, they inspired their troops to conquer their fear and accomplish goals thought impossible. Within civilian society, these figures corralled diverse goals and opinions into a powerful, unified focus. Once organized, these social entities became capable of pushing their society steadily into the bright future they all hoped to visit.