Pestilence means a deadly and overwhelming disease that affects an entire community. The Black Plague, a disease that killed over thirty percent of Europe's population, was certainly a pestilence.
Pestilence is also one of the four Horseman of the Apocalypse in the book of Revelation (which is part of The Bible). When pestilence rides into town, you want to be somewhere far, far away. Whereas a person gets the flue, a nation experiences a pestilence. A disease that causes widespread crop damage or animal deaths can also be called a pestilence.