The intergalactic void, or extragalactic space, is the space between galaxies. With respect to the Milky Way Galaxy, it was defined as being outside the galactic barrier. (DIS: "The Galactic Barrier")
According to Kelinda, the Kelvans that the USS Enterprise encountered in 2268 were born in the intergalactic void between the Milky Way and Andromeda Galaxies, and would die there on the way back to Kelva. (TOS: "By Any Other Name")
Sometime prior to 2364, the USS Greyhound encountered the extra galactic probe which was sent to the Milky Way Galaxy from outside the galaxy. (TNG: "The Last Outpost", "Datalore", "Conspiracy")
In 2369, around the same time the USS Enterprise-D visited Relay Station 47, the CGN Caroliqe was in this space. It was assigned to a deep space exploration of Sector 80912. (TNG: "Aquiel")