The word Terret comes from the Old French word toret/touret. It simply means small and round. This perfectly describes a terret. They are metal 
loops used on a horses harness. The reins or lines are passed through it to prevent tangling, or for them getting caught on the harness or shafts. On occasion a teret is U shaped or even square but the majority are round. There will be usually two pairs of terrets. One is on the harness saddle and the other an the hames of a collar both of which are used on horses pulling a vehicle. The vehicle could be a trap, chariot, carts etc.
Today and modern history have them made of brass or steel. However, in the Iron age they would most commonly be made of Bronze.
Fly terrets were introduced to help discourage flies bothering horses but in the 19th century they also had a decorative role. Fly terrets and brasses in their ornamental status were very popular from 1850 through to 1910.
Decorative mounts could also be found on saddles and armour for the cavalry. These are seen from prehistoric chariots, Cavalry from the romans to Napoleonic wars, through to the
decorative eras of the Victorians. Many dressage events today have polished up decorative items in their harnesses and saddles.
In the Stewartry museum there are some beautiful terrets and some very decorative mounts on display within the Treasure trove displays.