Final answer:
The mitochondria are the double-membraned organelles responsible for ATP synthesis. They contain folds known as cristae for increasing surface area for respiration and have their own DNA and ribosomes.
Step-by-step explanation:
The organelle that possesses a double membrane allowing gradient creation for ATP synthesis is the mitochondria. These 'power plants' of the cell have an outer membrane and a highly folded inner membrane called cristae, which increases the surface area for cellular respiration. This structure is crucial for the production of ATP, the energy currency of the cell, through processes that take place on the inner membrane. Moreover, mitochondria have their own DNA and ribosomes, resembling bacterial cells which support the endosymbiotic theory.