Definition of Warrant
A warrant is a court order signed by a judge that allows the police or another law enforcement officer to arrest a suspect or conduct a search on private property. The need for a warrant is established by the 4th Amendment to the U.S. constitution which places limits on the power of the police to make arrests, search people and their property, and seize objects and contraband without cause.
Prior to getting a warrant an affidavit must be issued which seeks the warrant and establishes probable cause for the requested action. If it is a search warrant it notifies the property owner why the search warrant was issued, such as searching for contraband or evidence of criminal activities.
A judge can issue a search warrant if they believe that there is evidence a crime has taken place or there is evidence from a crime that can be found on the property. The judge can come to this conclusion based on information provided by the police officer or from another person's observations (if they are considered reliable).
If the police office fails to get a search warrant and finds evidence the search is considered "unreasonable" and the evidence can be thrown out of court if challenged by the defendant.