Vertical separation is the separation of aircraft expressed in vertical distance. Vertical separation is established by the assignment of different altitudes or flight levels by air traffic control (ATC) to aircraft flying. The term vertical separation is more commonly used by ATC, since they are the agency responsible for maintaining separation between IFR (instrument flight referencing) and VFR (visual flight referencing) aircraft.
All the vertical separation guidelines can be found in the ATC manual 7110.65; chapter 4, section 5, paragraph 1. According to the manual, in order to have vertical separation, ATC must maintain at least 1000 ft of vertical distance between all aircraft within a 5 nautical mile radius of each other up to 41,000 ft. For example, if you have two aircraft, and they are flying within 5 nautical miles of each other with one aircraft at 10,000 ft, the other aircraft must either be at 9,000 ft and below or 11,000 ft and above.
Vertical separation can be canceled between two aircraft provided at least one of them is operating under VFR rules and that same aircraft reports having the other aircraft in sight. In a situation like this, the ATC would ask the VFR aircraft if they have their traffic in sight, and providing the aircraft replied by having traffic, the ATC would say, "maintain visual separation from that traffic." This absolves ATC of all vertical separation rules and only requires them to prevent an accident or incident from occurring.