When one century is ending and a new one is beginning, you can describe the time period as the turn of the century. Things that happened in 1902 occurred during the turn of the century.
The transition from one century to the next, and the period of time just after this happens, is the turn of the century. Typically, historians consider this period to comprise about ten years after (and sometimes ten years before) the start of the new century. So you can talk about dates like 1700, 2004, and 1399 as turn of the century eras.