If something happens precipitously, it's extremely sudden and maybe even a little shocking. When temperatures rise precipitously in the winter, the melting snow can cause dangerous flooding.
The adverb precipitously is useful for perilously steep things, like when you nervously park your car on a precipitously sloping San Francisco hill. It's good for describing abrupt changes too, like a precipitously plunging stock market. It can also be used to mean "carelessly," so your driving teacher may warn, "Don't swerve precipitously when you see a bicycle — just slow down."