The experiments were conducted by Jeff Steinhauer from the Technion-Israel Institute of Technology, using an analogue black hole in an "atomic Bose-Einstein condensate" -- a state where gas bosons are cooled to near absolute zero. It took Steinhauer seven years to perfect his sonic black hole to the point where it was accurate enough to mimic a real cosmic event horizon. Steinhauer was then able to observe phonons (particles of sound) behave at the black hole's event horizon -- and they did so according to Hawking's theory.
Hawking radiation suggests that a photon pair at the edge of a black hole would split. The negative photon would be swallowed, and the positive photon would be emitted as radiation. This means if a black hole isn't gaining mass from any other source, eventually it could shrink itself out of existence. The results of Steinhauer's experiments are the strongest evidence supporting Hawking radiation so far, but until physicists can measure Hawking radiation in a real black hole (no mean feat), it's a promising start.