Reionisation occurred in an early period in the history of the universe when the radiation from the first stars and first quasars started to cause substantial reionisation of the neutral atoms formed during recombination around 380,000 years after the Big Bang.
These first stars are hypothetically very massive, so-called population III stars, which are supposed to have shone for a brief period in time (less than I million years each). In the theory of stellar evolution it is well known that the more massive a star the faster it consumes its thermonuclear fuel. These population III stars therefore ceased to exist a long time ago and are perhaps at the origin of very distant gamma-ray bursts.
The exact date of reionisation is debatable because measurements provided by WMAP and the study of the Lyman-Alpha ray forests produced by the light from quasars do not correspond. All that can be said is that it probably happened between 100 and 400 million years after the Big Bang.