What is Arrest Warrant?

Legal Definition
An arrest warrant is a warrant issued by a judge or magistrate on behalf of the state, which authorizes the arrest and detention of an individual, or the search and seizure of an individual's property.
-- Wikipedia
Legal Definition
An arrest warrant is a document issued by a judge or magistrate that authorizes the police to take someone accused of a crime into custody. An arrest warrant is issued by the competent authority upon a showing of probable cause, which means a warrant may be issued if a reasonable person would believe the information at hand is sufficient to suggest criminal activities.

Arrest warrants serve the purpose of protecting people from unlawful arrests under the Fourth Amendment. The warrant also gives an actual notice to the person or persons being arrested about the charges pressed.

An arrest warrant is preferred but not required to make an lawful arrest.
See also
Legal Definition
A court order given to detain a party if probable cause is present. AKA warrant for arrest.