The words "bomb" and "cyclone" are bad enough on their own. What does it mean when they're used to describe a storm?

The East Coast is experiencing the early stages of what could be a whiplash-inducing stretch of winter weather

The U.S. East Coast is experiencing a whiplash-inducing stretch of winter weather. That's due in part to an atmospheric river and developing bomb cyclone.

A ‘bomb cyclone’ storm riding a 2,000-mile ‘atmospheric river’ threatens millions of Americans with power outages, toppling trees and ‘life-threatening floods’. Torrents of rain will drench swaths of the US as an ‘unusually potent’ weather system smashes in from the Caribbean.

The U.S. East Coast is due for a whiplash-inducing stretch of weather that will be rainy, windy and potentially dangerous, due in part to an atmospheric river and developing bomb cyclone. The storm is expected to bring heavy rain and fierce winds to many areas from Tuesday night to Wednesday night,

A wind and rain storm increasing in intensity throughout the day could cause flooding and power outages in Maine.