Where it is
USGS places the New Madrid seismic zone in southeastern Missouri, northeastern Arkansas, and adjacent parts of Tennessee and Kentucky. The 1811–1812 earthquakes were felt far beyond that area. USGS says they caused minor structural damage as far as Cincinnati and St. Louis and were felt as far as Hartford, Charleston, and New Orleans. In the New Madrid region they changed the landscape: bank failures, landslides, uplift and subsidence, and liquefaction. One uplift temporarily made the Mississippi River flow backwards, in the USGS account.
The three main earthquakes
The USGS science page on the 1811–1812 sequence lists three large earthquakes: about M7.5 on 16 December 1811, about M7.3 on 23 January 1812, and about M7.5 on 7 February 1812. The summary page explains why the magnitudes are estimates. There were no seismographs in North America at the time, so the sizes come from accounts of shaking and damage. The preferred values cited there are the ones used for the 2014 USGS National Seismic Hazard Map research. The zone overview page summarizes the same winter as three very large earthquakes estimated between magnitude 7 and 8. Use the tilde. These are not instrumental magnitudes like the 1960 Chile earthquake.
Why it is on a Ring of Fire site
It is the contrast. Every Ring of Fire rectangle on this site is a Pacific rim box. The central United States is outside all of them. New Madrid earthquakes are intraplate: they occur in the interior of the North American plate, along old buried structure, not at a subduction trench. A large intraplate earthquake can be felt over a wider area than a plate-boundary earthquake of similar size in the western United States, which is the comparison USGS draws with the 1964 Alaska and 1906 San Francisco shaking areas. That comparison is about the 1811–1812 shaking, not a prediction.
The geologic record, USGS says, shows the zone has produced sequences of major earthquakes, including several of magnitude 7 to 8, over the past 4,500 years. This page stops there. It does not turn a past sequence into a date for the next one.