The 22nd century is the period between 2100-2200 AD. Nobita's great-great-grandson, Sewashi, lives in the 22nd century. Doraemon came from the 22nd century using a time machine to Nobita's childhood period to help him.
The 22nd century is more scientifically advanced than the 21st century, thus allowing robots like Doraemon and Dorami to use many gadgets and tools.