The (nearly) 6000 years since the creation are divided into three 2000-year periods (see Talmud Rosh Ha-Shanah 31a, Sanhedrin 97a, and Avodah Zarah 9a). The first, called the period of chaos (tohu), began with the Creation and ended when Abraham was about 50 years old. The second, called the period of Torah, began with Abraham and ended shortly after the editing of the Mishnah, around 220 C.E., by Rabbi Yehudah ha-Nasi, thus codifying the Oral Torah. The third period is called "the days of Moshiach" because the Messiah could potentially have come at any time during that period. Note that less than 240 years remain in the third period. At the end of the 6000 years the world as we know it is expected to come to an end.
Ask a follow-up question