When English speakers say "20th century", it means the years from 1901-2000. Similarly, "18th century" is 1701-1800, and "first centry" is 1-100 A.D.
You can use this phrase as an adjective like this:
They discovered the sunken remains of a fifteenth-century trading ship.
They didn't have our modern 21st-century conveniences back then.
Without the hyphen ("-"), you can use this phrase as a noun too:
They've been fighting off and on since the 17th century.