Heroes are special units. They cannot be produced in cities, but must be hired or summoned. They have special abilities that can make them powerful in combat and some may cast spells. They can level up higher than normal units and may use magical items to further augment their power. A well-equipped, high-level hero is a valuable addition to your armies.
Acquiring a Hero
Heroes can be gained in several ways. Some heroes approach you directly (at the beginning of your turn) to offer their services. They will ask for a one-time fee, the size of which depends on the hero's strength. You will only receive the offer if you have sufficient funds, so keep some money at hand.
Heroes can also be summoned. The Arcane Spells Summon Hero and Summon Champion will do just that, the latter summoning a hero of greater power. These heroes require no fee, but of course the spells require mana to cast.
Finally, heroes can be found in towers and monster lairs. When defeating the monster, you will sometimes get the message You have freed a prisoner. This hero will offer to join your cause at no cost.
All heroes do require an upkeep on a turn basis. The price of this depends on the strength of the hero.
Heroes have the same type of stats as normal units (attack, defense, etc). They are usually quite strong units, although they can be defeated by regular troops, especially when on their lower levels. What makes them really bad-ass is their special abilities.
Some abilities give a bonus at each level. E.g. Might gives +1 to melee attack at each level of the hero. These abilities can add up quickly, making the hero very powerful indeed.
Heroes can gain the same attack types as regular units, such as Thrown, Poison, Illusion and Armor Piercing. Combined with their naturally high attack, this can make heroes frighteningly efficient.
These abilities give a bonus to your domain, regardless of the position of the hero. These include Sage (bonus research), Noble (Bonus income) and Legendary (Bonus fame). The bonus they give will increase with levels and can make a big difference, especially early on.
Some abilities give bonuses to all units stacked with the hero. Leadership gives an attack bonus, Armsmaster provides extra experience to units. Some of these allow for swifter movement; Mountaineer and Forester allows fast movement over these types of terrain. Used wisely, this can be used to escort otherwise slow units quickly to the enemy.
Some abilities are harder to categorize. E.g. Caster turns the hero into a minor wizard. In combat, this hero can cast spells independently of your own wizard powers, allowing you to cast two spells in the same turn. If placed in your capital, the hero will add half of his caster skill to your spell skill, allowing you to cast overland spells quicker.
Heroes can carry magical items that you either find or forge. Each hero can carry only three items and are limited in the type they can use. Only wizardly heroes can use staffs and wands, only archer heroes can use bows. Magical items can give bonuses and special abilities in addition to those of the hero, adding further power.
Losing a Hero
Heroes can be killed in combat like any other unit. Once killed, the hero is out of the game and will not reappear. The Life spell Resurrection will allow you to bring back a dead hero, but otherwise, you're out of luck. Protect your heroes by stacking them with strong units and giving them protective magical items.
Torin, the Chosen
Torin is a special hero. He cannot be acquired by the normal means, but only through the Life spell Incarnation, which summons him. He further has the special ability that he can be summoned over and over. If he dies, you can simply summon him again. He will retain the experience that he earned in his past incarnation. Needless to say, Torin is a very strong hero.
This site has a decent overview of all the available heroes, including their stats, abilities and growth potential.