An arrest warrant is an official document, signed by a judge (or magistrate), which authorizes a police officer to arrest the person or people named in the warrant. Warrants typically identify the crime for which an arrest has been authorized, and may restrict the manner in which an arrest may be made. For example, a warrant may state that a suspect can be arrested "only between the hours of 6 a.m. and 6 p.m." Finally, some warrants also specify the bail that a defendant must post to regain freedom following arrest. If the warrant is for a previous failure of the suspect to appear in court—called a bench warrant—it will probably specify that the arrested person may not be released on bail at all (sometimes termed a "no-bail warrant").
To obtain a warrant, a police officer typically submits a written affidavit to a judge or magistrate. The affidavit, given under oath, must recite sufficient factual information to establish probable cause that a crime was committed and that the person named in the warrant committed it. A description so broad that it could apply to hundreds of people will not suffice.
For instance, a judge will not issue a warrant to arrest "Rich Johnson" based on an affidavit that "a liquor store was held up by a bald, potbellied man of medium height, and Rich Johnson matches that description." That description doesn't establish probable cause to believe that Rich Johnson robbed the liquor store, because the vague description would apply to numerous people. On the other hand, probable cause to arrest Rich Johnson probably would be adequate if the affidavit included the factual information that "the liquor store clerk and three witnesses identified a photo of Rich Johnson as the person who held up the liquor store."
Sometimes, arrest warrants contain factual mistakes. For example, the suspect's name may be misspelled or the wrong crime may be specified. Ideally, the police should show the warrant to the suspect. And, if the suspect is able to prove that the officer has the wrong person, then the officer should not proceed. As a practical matter, however, the police sometimes don't show the warrant to the suspect for a variety of reasons real or imagined, and any mistakes as to identity are sorted out later. As for clerical errors, these aren't enough to invalidate the warrant.