The main purpose of the registered agent is to receive official communications from the state and to receive service of process. By having a person designated to receive service of process within the state, your business is essentially consenting to the general jurisdiction of the courts in that state. The appropriate departments of the state government will direct communications to the registered agent.
The requirements for a registered agent are determined by state law, so there can be some variation. Generally, the registered agent can be an individual person who is a citizen of the state or a business organized in the state or registered to do business in the state. The registered agent must be available during normal business hours to receive service of process.
The registered agent requirement usually goes in tandem with the requirement for a physical address within the state. Generally, the address cannot simply be a PO box, but must be a location in the state where the registered agent is available during normal business hours. The address must be within the state so that service of process on the registered agent at that location will establish the jurisdiction of the state's courts. The address usually does not have to be a principal place of business, however.
Though it's common to have a member of the LLC act as the registered agent, there are several reasons why businesses choose to pay for a registered agent service. An obvious one is when the there is no one closely associated to the business in the state. However, using a separate registered agent also adds a layer of privacy to the business, since the name and address of the agent becomes public record. Having a separate registered agent also allows the business owner to keep flexible business hours and avoids potentially embarrassing service of process in front of employees or family members.