A Detaining Power is the country, state, government, or any other jurisdiction which detains, holds, or incarcerates those who are alleged to have committed an offence against this jurisdiction

Jurisdiction

Jurisdiction is the practical authority granted to a formally constituted legal body or to a political leader to deal with and make pronouncements on legal matters and, by implication, to administer justice within a defined area of responsibility...

 or others (which for whatever reason have not been or will be proven not to be fit to process the detainees in question). In short, anyone who prevents someone from leaving a country or state and may have lawfully arrested and held such persons for a length of time may be referred to as a Detaining Power.

For legal purposes, it is a condition of the 3rd drafting of the Geneva Agreement that a detainee may request that their crimes be proven to justify their incarceration.

At time of submission the Quirin case and the Guantanamo Bay

Guantanamo Bay detainment camp

The Guantanamo Bay detention camp is a detainment and interrogation facility of the United States located within Guantanamo Bay Naval Base, Cuba. The facility was established in 2002 by the Bush Administration to hold detainees from the war in Afghanistan and later Iraq...

trials are examples of highly disputed Detaning Power in the US and under the US jurisdiction.