A century is 100 miles done in one day (24 hours?) but more or less as all-at-once as possible. In other words, riding 50 miles on Saturday going home, sleeping the night, etc. and then finishing the remaining 50 miles on Sunday wouldn't be considered a century .... however riding 50 miles, then stopping for lunch in a cafe, and finishing the 50 miles probably would be considered a century.
Some suggest that a "day" is 12 hours, but I've done century at -32C on ice and snow that took me 15 hours so I prefer to call a "day" a 24-hour period to allow for extreme conditions which require slower riding and a few more brief breaks than a person might take on a century on a lovely sunny warm day.
It can be an event organized by a club or whatever, or it can be just you on the bicycle riding 100 miles.
Double century = 200 miles
Back-to-back century = a century on one day, and another century on the next day
Metric century = 100 km
Double metric = 200 km