They are knights that have red helmets and wear white (sometimes they have a red and white shield with them (they aren't holding them though)). You will know you are fighting a Templar because they make really weird sounds instead of talking and you get a little message when you kill them.
Early on you should try avoiding them unless you are pretty good at fighting or you can sneak up and assassinate them (one hit kill) as they are as tough as old Thatcher.
They are based on the real Knights Templar, for info see your local google.
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"The most merciful thing is the inability of the human mind to correlate all its contents"
Well if you have the skills of an assassin like I do then you just eliminate them without them knowing. I had to do it for a side quest so I could get some info.