What type of connector is this and how do I remove it?
It's a push-in wire connector, like these from Ideal.



The wire should come out without too much difficulty; grip the connector firmly in one hand, then pull the wire with the other.  

The instructions for the Ideal connectors that I linked to say:


  7. In order to remove a wire, pull and twist the wire back and forth.


Since you're installing a new light fixture, this is also relevant:


  6. Connector is reusable on solid wires of the same wire gauge or larger.  If reusing connector, cut and re-strip conductor.