In the Extraordinary Form of the Mass, the days leading up to Ascension Thursday are designated to pray for the blessing of crops and also for safety from natural disasters. Fr. Z writes about it here.
The name "Rogation" comes from the Latin "rogare", to ask. Rogation Days originated in the the fifth century, when a Diocese in France was experiencing earthquakes and "other calamities", and was then later introduced into the Church's general observance by Pope Leo III.
The Litany of the Saints, psalms, and Mass is celebrated, along with a procession. A fast and/or penances may also be observed by the faithful.
I'll be saying the Litany tonight when I pray for those people in Springfield; and a prayer of thanksgiving that Fairfield County was spared.