The 22nd century is the period between 2101-2200 AD. Nobita's great-great-grandson, Sewashi lives in the 22nd century. Doraemon had come to Nobita from the 22nd century using a time machine.
The 22nd century is much more scientifically advanced than the 21st century. That's why so wonderful robots like Doraemon and Dorami would be made during this century.