What souls are
Souls buy items and also level up your hero and abilities. The team with more souls usually wins the fights.
Last hits and securing souls
The killing blow on lane troops gives the most souls. Part of the reward appears as a small orb you claim by shooting it; if the enemy hits it first, it is denied.
Neutral camps
Camps between the lanes are extra income. When your lane is safe, clearing the nearest camp turns idle time into farm.
The cost of dying
Every death costs respawn time and feeds the enemy souls. Backing off with low health is often worth more than a risky kill.