Dark space (or intergalactic space) is the name of the physical space between galaxies in the same way as interstellar space is the space between stars within a galaxy. Dark space is completely dark, as it contains little to no stars and makes up almost the entire volume of the universe, where galaxies are only small islands of light. The distance between two neighboring galaxies is in the order of several million light-years, while the diameter of the Milky Way's galactic disc is only about 100,000 light-years.
According to Vigil, the Reapers go into long states of hibernation to conserve energy. However, in this state they are vulnerable. By taking refuge in dark space beyond the galaxy's horizon, the Reapers ensure they will not be discovered by accident and destroyed while they wait for their vanguard to open the Citadel mass relay, allowing them to return to the heart of the galaxy.
The last attempt to open the relay to dark space ends in victory for the assembled organic forces and the Reaper vanguard's destruction. Whomever is chosen to be the human representative on the Citadel Council, either Donnel Udina or David Anderson, swears to lead the galaxy against the Reapers and "drive them back into dark space."
Collector Base, the Reaper fleet is seen out in dark space moving towards the Milky Way. The Reaper fleet had apparently already been in transit towards the galaxy since Shepard destroyed Sovereign.