The vents or hot vents are located in Seattle Grace Hospital and the hospitals later established in the building, presumably in the basement. They've grown to become a special place for Cristina and Owen.
After fighting with Meredith and about to cry, Owen led Cristina to the vents and asked her to wait. After a few moments, the air blew up from underneath her and she felt better. Whenever they had problems, they would go there and it would make them feel better. Later, it is also where Cristina told Owen she loved him.
Cristina also brought Izzie there when Izzie told Cristina about her cancer.
It is also where Cristina and Owen had sex in the episode State of Love and Trust and Cristina got vent marks burned into her ass.
Owen takes Cristina to the vent to celebrate her Harper Avery Award nomination.
After contemplating dating again, Owen goes to the vents where he imagines Cristina being with him as he remembers their encounters there.