Jeremy,
That part connects to the moveit warehouse. If you are connected to the warehouse database (first tab of the plugin), the constraints table is read and the names of the constraints are used to populate the list you mention.
Note: planning with constraints requires a fast IK solver that is also able to find the solution nearest to the seed state.
Populating that database can be done programmatically using the ConstraintsStorage class. For an example, take a look at moveit_ros/warehouse/warehouse/src/initialize_demo_db.cpp
There is also a launch file in your config package: default_warehouse_db.launch;