Why does the "Ring of Fire" pretty much define "Pacific Rim"
There isn't a concentration of tectonic plates - rather the opposite!

The "Ring of Fire" is a pattern really. It is marked by subduction zones. So the question becomes, "Why is the Pacific Ocean surrounded by subduction zones?".

Think back to Pangaea. This was a supercontinent that formed in the late Palaeozoic. Virtually all of the Earth's land masses were concentrated in one large supercontinent. When this broke up, the new continents moved away from each other. Fast forward 200Ma or so, and you find that the continents have moved so far apart that they are now converging on a point on the other side of the planet - the continents are moving towards each other! Hence the remains of the super ocean (which was actually multiple ocean plates - today's Pacific &amp; Nazca plates, plus the Farrallon plate (RIP),etc ) is shrinking as the continental plates move towards it.
This destruction of the ocean plate(s) occurs at subduction zones.

This is a big picture generalisation. Not all of the Pacific's boundaries are marked with subduction zones (e.g. North America has two large strike slip systems + a new spreading ridge). Also, not all of the continents are converging on each other. Africa is doing a pirouette, India is moving northwards, etc.