A crown is a dental restoration indicated when a tooth has become cracked, fractured or is in danger of cracking or fracturing due to a weakened state. A tooth with a crack can be temperature sensitive or give a sharp painful "ZAP" when biting. A cracked tooth can be crowned and hopefully the nerve of the tooth can be protected ,reinforcing the tooth so the crack does not worsen. If the crack is deep enough the nerve of the tooth can be affected resulting in the need to treat the nerve with Root Canal Therapy (RCT). If the crack is bad enough the tooth could even be lost.
Other things that can weaken a tooth are very large existing fillings that are failing, previous Root Canal Treatment, or a tooth with a large amount of decay. It's all about how much tooth structure is left and how strong that tooth structure remains. Bonded restorations (White Fillings) are excellent for reinforcing a fragile tooth but they do require strong walls to bond to.
So a crown is basically a "Helmet" that goes over the top of a tooth in order to reinforce and protect the remaining tooth structure. Other reasons a crown could be done for a tooth include cosmetics or to change the shape or size of a tooth.
I hope I have helped to inform those inquiring minds!