Q:

How do I change these MR16 light fittings to GU10? ( pics included)

I'm looking to change to GU10 from MR16. 
I bought this: https://www.amazon.co.uk/gp/product/B0785RKFNN/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
I've circled in blue where I attached the new GU10 lamp holder.  I plugged in a GU10 bulb and the light doesn't come on. 
What's going on here? 

A:

In general, MR16 bulbs use 12 volts, which is the reason for the transformer (white box).  GU10 bulbs, on the other hand, generally run directly on mains voltage (120 or 240 volts).  So you are feeding 12 volts into a 120 or 240 volt bulb and it is barely light, maybe not visibly. 
You need to look at the markings on the bulb and verify its voltage.  If it is mains voltage, you need to remove the transformer and splice directly into the wires from the ceiling.