BigiQ use a REST API to manage and communicate with the BigIP devices once they are added to the Big-IQ management UI. The BigIP devices needs to be running version 11.3 or later for Big-IQ to manage them.
For Big-IQ version prior to 4.3, you would need to install the Big IQ REST API framework on each Big IP device using a script in TMOS under the /usr/lib/dco/packages/upd-adc dir
./update_bigip.sh –a admin –p password . with 4.3 that can be done from the Big IQ UI.
When that is done, you will need add Big-IP devices to the Big-IQ either in the cloud or device UI depending on what you are trying to do.
Once the Big-IP devices are added, you will have access to application health stats and HW stats such as CPU, Mem, HDD etc..
Additionally you can directly manage the Big IP devices using iControl REST as you mentioned
Hope this helps