As part of hurricane missions, the hunter aircraft drop sounding beacons at times to get readings of wind, temperature and moisture at different heights. It collectively helps create a better picture of the environment the storm is in. They realized the data they look for could be helpful outside a hurricane, since they were still looking for some of the same things! TLDR, feeding actual, fresh human observations helps the computers a lot more than when they work off their own previous guesses. This is why we fly the planes into the hurricanes in the first place. It directly means better forecasts, which directly saves lives. Every last digit of automated info the planes record is invaluable.
Warmer water in general holds more heat. More heat, for coastal storms, can equal more energy, so more precipitation over land. If you've ever heard about hurricanes strengthening over the Gulf Stream, this is why! It's a unique feature of warmer water over a relatively narrow area.
Well, that thing is on steroids right now compared to where it should be for this time of year. So versus this same storm in another year it has a lot more energy to work with. The water off the coast of the northeast is warmer than usual, too. The warmer area was farther north last year and contributed to Boston's record snow. The storm is going to move over all of that. The longer it hangs around the more people get snow. If the storm moves away faster (which is what some other models are saying), less snow. The Gulf of Mexico, where it's drawing from already, is a common home of extra heat, too.
There's a big line of warm water going up the coast and then a pool off the cost of Long Island just begging to get used up. How much energy the storm has the more snow total it can dump out. Different computer models might factor this in differently when it gives estimates, and the fewer examples of past storms the more they have to wing it. Thus, anywhere from 3-28" for NYC and 0-18" for Boston depending on which computer you ask. The only thing to nearly certain of for now is that DC is doomed. The computers cough out new data every 6 hours. The first model that was fed that aircraft data dramatically increased some snow totals, which is the current concern.