The time of day when the TV audience is at its largest.
We now associate the term 'prime time' with TV ratings and advertising, i.e. the prime slot for the placing of TV adverts. In that context it originated in the USA soon after WWII. For example, this piece from The Wall Street Journal, January 1947:
"Columbia Broadcasting System, for instance, has an unsold hour of prime time on Tuesday nights, beginning at 9:30."
A prior usage of 'prime time' had been coined many centuries earlier, to mean Spring or 'at the beginning' (of the day, of life etc.). It is likely to have been inherited into English from the French word for Spring - Printemps. Geoffrey Chaucer used the term in the late 14th century, in his translation of the French lyric poem The Romance of the Rose:
"Daunger... is feers of his cheer, At prime temps, Love to manace. " &
"Pryme temps full of frostes whit, And May devoide of al delit."
By the 16th century, the Anglicization to 'prime time' was complete, as in this example from Edward Hall's The Union of the Noble and Illustre Famelies of Lancastre and York, 1548:
"In ye pryme tyme of the yere he toke his iorney towardes Yorke." [In the Spring he took his journey to York]
Many European languages have had a form of 'prime' meaning 'first/primary', for example, 'prime', in English/Middle Dutch/Middle German, 'prim', in Swedish/Danish/Icelandic, 'prima', in Spanish/Portuguese/Italian etc. These all stem from the Latin 'prima' (first hour).
In addition to the Chaucerian 'Spring', the Latin 'prima' was also the source of 'prime' as the name of the first of the canonical hours of prayer of the Catholic Church. This gave us a yet earlier meaning of 'prime time', i.e. 'early morning', the time when the first prayers were offered. Old English texts which include references to this 'prime' include The Rule of Saint Benedict, which dates from circa 530.