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Radiation era (aka radiation-dominated era) refers to a period after the Big Bang when the energy density of electromagnetic radiation was greater than the energy density of matter. As the universe expanded, some thousands of years after the Big Bang (one source says 47,000 years), this reversed, and subsequent time is termed the matter era or matter-dominated era. As the universe expanded, radiation energy density changed at a rate proportional to R-4 whereas that of matter changed at a rate proportional to R-3, allowing for the reversal (where R is the scale factor, an increasing number indicating the relative size of the universe as time passes). This change to the matter-dominated era occurred considerably after Big Bang nucleosynthesis (which took place over the first a few minutes after the Big Bang) and considerably before the recombination (which occurred 300,000+ years later).
Other names used for the radiation era include the radiation epoch, the photon epoch, and the photon era. The term primordial fireball is also used, but I've also seen this term specified as ending with the recombination.