The reason that this term is used to refer to the Pacific Rim geographical region is fairly straightforward. The area is referred to as the “Ring of Fire” because of its shape and because of the fact that it has a large number of volcanoes.
The Pacific Rim region has a shape that is roughly circular. There are land masses that surround the Pacific Ocean, making something of a circle. This is the likely reason for the use of the word “ring.”
The Pacific Rim region is also very seismically active. There are volcanoes (which, of course, can erupt in fire) in almost every area of the Pacific Rim. The only place that could be called part of the Pacific Rim but which has no volcanoes is Antarctica. There are volcanoes such as Mt. Rainier and Mt. Saint Helens in North America. There are volcanoes like Llaima in South America. There are volcanoes like Mt. Fuji in Japan and volcanic islands like Pagan in Micronesia. Most of the volcanism on the Ring of Fire is caused by the subduction of one plate under another.
Thus, this area is known as the “Ring of Fire” because it is a roughly circular area with volcanoes on almost every side.