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The first century included the years 1 to 100.
First century. A century is 100 years, and the first century is years 1-100. The second sentury is 101-200, etc.
The 20th century. We add 1 to the first two digits to get the century. This is since the first century is classed as the years 0 to 999, the 2nd century the years 1000 to 1999 etc.
Because years 1-100 are in the first century; years 101-200 are in the second century, and so on... 2010 is in the 21st century.
The year 79 A.D. was in the First Century. Years 0 to 99 AD were in the first century after the start of the calendar (supposedly the death of Christ) - hence the First Century.