A so-called ‘FISA Warrant’ is an order granted to The United States Foreign Intelligence Surveillance Court (FISC, also called the FISA Court). It was established and authorized under the Foreign Intelligence Surveillance Act of 1978 (FISA) to oversee requests for surveillance warrants against foreign spies inside the United States by federal law enforcement and intelligence agencies.
In order for FISC to issue a warrant, an application must be made before an individual judge of the court. The court may allow third parties to submit briefs as amici curiae. When the U.S. Attorney General determines that an emergency exists, the Attorney General may authorize the emergency employment of electronic surveillance before obtaining the necessary authorization from the FISC, if the Attorney General or their designee notifies a judge of the court at the time of authorization and applies for a warrant as soon as practicable but not more than 7 days after authorization of such surveillance, as required by 50 U.S.C. § 1805.
What all this complication means is that, ostensibly, to help the US obtain information on foreign government or individual activities, there is a process by which a warrant is issued to search or monitor. It is made through a Judge of the FISA Court and there is a process by which an appeal may be made.
Normally, the FISA warrant does not make news. However, in 2017 there is speculation surrounding President Trump and his advisors as to whether this means was utilized during the campaign of 2016 to gather information on foreign activities.