' The time between these two is the time for prayer.'"

Meaning Fajr, the morning prayer. The Fajr prayer was elongated because the Prophet recited at length during the prayer, so that it ended just before sunrise. That defined the end of the time for Fajr, as the beginning of the time was defined by the moment when he started the first Rak'ah.
Sunan an-Nasa'i Book 6, Hadith 20