Loyalty is an attribute of each city. Each city starts with 100% loyalty but can be lowered by attackers using chiefs. Once a city's loyalty reaches zero the city then joins the last attacker's account (the attacker that reduces the loyalty to below 0%).
Loyalty is regained from a palace or residence by 1% per level per hour (so a level 10 palace would regain 10% loyalty per hour).
During a chief attack, holding a great celebration at the attacked village will reduce the loss of loyalty up to 5%, and holding a great celebration at the attacking village (the village sending chiefs) can make the chief 5% more effective.