Heroes in the Total War: Warhammer are the equivalents of Agents from previous installments of the franchise. However, this time their role is more important - which you can learn from this chapter.
What are heroes
In Total War: Warhammer heroes are used to perform various tasks. The first and probably the most known to the fans of the Total War franchise is the ability to perform actions against enemy settlements, Lords and heroes. By doing so you can, for instance, attack the enemy Lord to inflict damage on his troops, decrease the Lord's movement speed on the map, or even kill the Lord. If the enemy Lord dies, the enemy will be forced to select a new Lord in his place, but he will lose all of the experience points accumulated, which can make that army a lot weaker.
Attacking settlements will allow the hero to inflict damage onto the soldiers garrisoned there, or damage one or multiple buildings - this will prevent the buildings from functioning normally until they are repaired. It's also a good method to ruin the economy of the enemy faction - repairing buildings can be extremely costly and forcing the enemy to do that multiple times will either cost him a lot of gold, or he will lose the buildings permanently. Additionally, a hero can be used to assassinate another hero - if he is successful, the targeted hero will die and disappear.
It's not all the heroes can offer. Aside from performing hostile actions against enemies, you can draft them into a Lord's army, where they will be, basically, mini-Lords. They can't command their own army, but in combat they are more powerful than most units in the game. Additionally, they have access to similar abilities that a "normal" Lord has. They can increase the effectiveness of other troops, or to boost discipline. What is more, some of them are capable of using magic (available spells depend on the type of hero-mage) - it's useful especially when your Lord is incapable of casting spells.
Another function of a hero is his influence over a province. Their mere presence has huge impact on the province, like influencing corruption (either increasing it or reducing, depending on the faction you're playing), public order, the causality replenishment rate, income from trade and other constructions, and so on. Additionally, they have negative influence over enemy provinces - they can decrease their income or public order, or increase corruption.
Heroes, although extremely powerful, aren't available from the start. To gain access to their services you must first construct specific buildings. Each faction has access to a number of different types of heroes (like 3 different mages in the Empire) and each one of them will require a different building - you can check it in the building's description. If you want to recruit a hero, select any settlement in a province that has the required building constructed (or a Horde that has access to a hero - if you're playing Warriors of Chaos) and press the first button from the right on the bottom of the province / horde screen. Hero recruitment screen will be then displayed.
However, those hero-recruiting buildings influence only the province they are constructed in. If you construct a building allowing you to recruit a specific hero in one province, you will be able to recruit them only in that province. However, those buildings offer a lot of different bonuses as well - decreasing / increasing (depending on your faction) corruption in a province, or in adjacent provinces.
Another way to gain heroes is to complete quests that are assigned from time to time. For completing objectives (like defeating a specific enemy, conquering a given settlement, or sending your hero to a specific place on the map) you will be given a large sum of gold and sometimes a free hero.