The Yamato period is named after the Yamato province where, during this time period, the Imperial Court ruled. The Yamato Province is located in today's Nara Basin. During this time period, the Yamato government took hold of western Japan through negotiations and warfare. The Yamato seemed to have defeated a rival power group located in Izumo.
During this time period ruled the first verifiable emperor, Suijin. Whereas the Nihon Shoki claims that Emperor Suijin was the 10th emperor, and that he died in 30 AD, however he is the first emperor of Japan whose existence can be verified, and his death was most likely in 318 AD. Using the texts Nihon Shoki and Kojiki are very unreliable as they were written around the year 700 AD.
The Yamato Period can generally be divided into the Kofun Period and the Asuka Period. However, the exact dates are a bit blurry because the Kofun and Asuka Periods aren't mutually exclusive. That is, the Kofun period is more of a cultural / archaeological time frame, whereas the Asuka Period is more of a political / historical time frame; the two overlap to some degree.