The epoch of reionization (or just reionization or the era of reionization) is a period in the history of the universe that occurred sometime within about 6 < redshift < 20 (or 6-15, cited boundaries vary) when hydrogen atoms split with their electrons. Though this was not instant, for some purposes it can be treated as a point in time.
The period of time immediately before it is called the dark age. Just before that, at z = 1089, 378k years after the Big Bang, hydrogen went from ionized to neutral, i.e., recombination. Neutral hydrogen is transparent whereas free electrons scatter photons, making the universe opaque. When galaxies formed, their ultraviolet electromagnetic radiation ionized the hydrogen again, i.e., reionization. At that time, universe remained transparent because electrons were sufficiently far apart that the scattering is sporadic. The dark age was named because there were no sources of light, i.e., no stars.
Reionization is studied by studying quasars and Population III stars, as well as the cosmic microwave background.