The term Quaternary (fourth) was proposed by Jules Desnoyers in 1929 to address sediments of France's Seine Basin that seemed clearly to be younger than Tertiary Period rocks. The Quaternary Period follows the Tertiary Period and extends to the present. The Quaternary roughly covers the time span of recent glaciations including the last glacial retreat.
The 1.6 million years of the Quaternary represents the time during which recognizable humans existed. Continental drift is largely irrelevant to a period so short. The climate was one of periodic glaciations with continental glaciers moving as far South as 40 degrees latitude. Few major new animals evolved, again presumably because of the short -- in geologic terms -- duration of the period. There was a major extinction of large mammals in Northern areas at the end of the Pleistocene. Many forms such as the saber tooth cat, Mammoths, Mastodons, Glyptodonts, etc became extinct worldwide. Others including horses, camels and cheetahs became extinct in North America.
Quaternary should not be confused with the mathematical quantity known as a quaternion.