What would the advantages be of creating a space colony?

The specific advantages of a particular space colony will possibly change depending on where the space colony is located. That's one unknown variable in this question. Does "space colony" refer to some kind of station in the vacuum of space, or does it open up the possibility for a colony on a moon, planet, or asteroid? Another variable in the question would be how large the space colony would be. I'll try to provide some broad advantages that might cover multiple types of colonies.  

Population control on Earth. Earth has a finite amount of space available for living, food production, etc. It also has a finite amount of energy providing substances. At some point, Earth is going to reach its human-carrying capacity. If large parts of the human population are moved off of Earth, the point at which we reach the carrying capacity could be delayed.  

Provide resources that are lacking on Earth. More and more is being demanded of Earth's limited resources. A space colony could provide Earth with more of those resources. Plenty of asteroids are rich with materials that are in high demand on Earth. A space colony could function as an off-world mining facility to harvest those materials and send them to Earth.  

Isolation protection for a group of humans. A space colony would be completely isolated from Earth. That means any species-ending catastrophe that happened to Earth (nuclear disaster, pandemic, etc.) wouldn't affect those humans that are on the space colony. The space colony would ensure that the survival of a species continues.