Reionization is a process that occurs after the epoch of galaxy formation begins, and is the second of two major phase changes of hydrogen gas in the universe. The first is recombination, happening at a redshift z = 1000 (400,000 years after the big bang), at which time the cooling due to the expansion of the universe brought it to a temperature such that the hydrogen recombination rate was greater than the ionization rate (the ionization rate increases with increasing temperature), allowing protons to recombine with electrons to form neutral atoms. The second phase change, reionization, is thought to have occurred when the first few generations of population III stars and quasars emitted radiation that reionized the universe, making it once again an ionized plasma (6 < z < 20; 150 million - one billion years after big bang).
The efficiency with which intervening gas between a quasar and an observer can absorb radiation at certain wavelengths, such as at the Lyman-alpha transition of atomic hydrogen, depends sensitively on the degree to which it is ionized. Due to the expansion of the universe however, these absorption features are redshifted more and more the farther from us that the absorption actually occurred, so that absorption features in different parts of the spectrum are produced by gas at different points along the line of sight. Since light from the quasar that reaches us now passed different points along the line of sight at different times, differing parts of the spectrum correspond to different times in the evolution of the universe. Looking at the spectrum of a quasar can therefore tell us not just spatial, but also temporal information with regard to the degree to which the universe is ionized.
In this way, it can be inferred from the lack of the appearance of a Gunn-Peterson trough of absorption in the spectrum of quasars at redshifts of less than z < 6 (seen as they were more than about one billion years after the big bang), that most of the intervening intergalactic medium since then consists not of neutral atoms (which would form a Gunn-Peterson trough) but rather of a highly-ionized plasma. The absorption lines seen in the spectra of such quasars, known as the Lyman-alpha forest, are due to absorption by a small but enhanced fraction of neutral gas lying in dense regions along the line of sight. Recent observations of quasars at redshifts slightly higher than z = 6, however, do show a Gunn-Peterson trough, indicating that the universe was at least a few percent neutral at that time.
Theoretical studies of reionization suggest that the universe should go from highly neutral to highly ionized in a relatively short period of time. The presence of a Gunn-Peterson trought in the spectra of quasars at z = 6, implying the universe was already a few percent neutral, indicated that perhaps reionization began not much earlier, and that the universe was mostly neutral at redshifts z > 10.
As of 2004, this has created a puzzle due to observations from WMAP, which measured the total number of electrons present in the universe since recombination. This measurement of the Thomson scattering optical depth to electrons implies that if reionization occurred abruptly, it had to begin and end at a much earlier time, z = 17 (about 200 million years after the big bang). This indicates that: (1) either the Gunn-Peterson or WMAP results are being mis-interpreted OR (2) that reionization does not happen abruptly but is long and complex. It would seem the best bet is that the theoretical models were too simple and that reionization is long and complex. Astronomers are in a frenzy to understand this.