Apparent authority is a type of agency power that arises when third party reasonably believes an agent or other actor has the authority to act on behalf of the principal and that belief is traceable to the principal's manifestations. Apparent authority typically becomes important where an agent purports to take some action on behalf of a principal, such as signing a contract, which the agent did not have actual authority to do. If the third party reasonably believes the agent has that authority, then the principal will be bound to the contract or other action even though the principal may have expressly forbidden the agent to take that action. Note that the reasonable belief of the third party must be traceable to the principal's manifestations, so an impostor masquerading as an agent with no endoresement of the principal will not have apparent authority.
Apparent authority is distinguished from actual authority, even though both have the same effect relative to third parties. Note that actual authority is based on the agent's reasonable belief about the agent's authority to take the action, whereas apparent authority is based on the third party's reasonable belief about the agent's authority to take the action.
The Restatement (Third) of Agency describes this in Comment c to Section 2.01 when it explains that in actual authority the agent has not only the power, but also the right to act on behalf of the principal. This is distinguished from apparent authority in which the agent has the power, but not the right to act on behalf of the principal.
The term ostensible authority is often used as a synonym for apparent authority. Other courts use the term ostensible authority to refer to estoppel in the agency context.