An Armada storm is basically a huge extreme hurricane/cyclone/typhoon. The name originated from newspaper article about one of the first Armada storms, which stated that if a butterfly could start a hurricane it must have taken an armada of butterflies to start the storm which had just passed.
Earth in the centuries leading up to the Night's Dawn period has suffered run-away global warming. The overuse of fossil fuels in the 20th and 21st centuries kick started the warming process off. As technology improved, with the advent of fusion energy, Earth saw the complete elimination of the use of carbon based fuels. However, the greenhouse effect now had Earth in a stranglehold. The Polar icecaps and mountain glaciers melted. This melting released enormous amounts of carbon in the form of carbon dioxide and methane from the deep ocean and tundra. As a result of having trillions of litres of fresh water dumped in to the ocean, the deep sea currents all shutdown. This impacted on the heat transfer mechanisms of the whole planet. In the past, the ocean currents transported heat from the tropics to the poles, thus distributing warmth - the tropics did not over heat and poles remained (slightly) warmer.
The end result, was that the ocean surfaces are now warmer - much warmer. Without deep sea currents to carry away the heat, plus a 40+ billion population consuming massive amounts of energy (which will eventaully get released as heat, no matter how that energy is produced in the first place), the end result is BIG. Hurricanes are powered by warm oceans, so a having a hot ocean will produce storms of a greater intensity. In terms of hurricanes, the average Armada storm is Category 7, and a big one, Category 12.
Why the Armada name? The term relates back to an old scientific theory, where the beat of a butterfly wing in one part of the world could create a storm in another part. (Chaos theory of atmospheric dynamics). When the first mega storm happened, a commentator said that a whole armada of butterflies must have beat their wings to create such a bad storm. The name stuck.