Here's another pic

This fixture needs to be mounted to a box.
If you have a black, white and ground in that box you connect white to white, black to black, and all three grounds together.

You keep referring to "outlet". Do you just mean the box, or is there actually a receptacle in the box?

The two ground wires are to make sure both large pieces that make up the light fixture remain safety grounded to the same point within the house electrical box providing the power at all times. Possible reasons: just electrical code regulations, or the light housing and the wall portion could made of different metals and need to be electrically isolated to prevent corrosion so two wires are needed, or they are made of different metals but not electrically isolated and will eventually corrode where they are in contact so two separate ground wires are needed.