Most often, the term warrant refers to a specific type of authorization: a writ issued by a competent officer, usually a judge or magistrate, which commands an otherwise illegal act and affords the person executing the writ protection from damages if the act is performed.
"This Court orders the Sheriff to find the named person, wherever he may be found, and deliver said person to the custody of the Court."
Warrants are also issued by other government entities, particularly legislatures, since most have the power to compel the attendance of their members. This is called a call of the house.
A warrant is a written legal document, issued by a judicial officer, directing a police officer to perform a specific action and affording said officer protection from damages if the act is performed.
Warrants are typically issued by courts but can also be issued by Congress and other political entities.
A typical arrest warrant will take the approximate form of: "This Court orders the Sheriff to find the named person, wherever he may be found, and deliver said person to the custody of the Court."