When there is a drought somewhere, there's not enough rainfall. In certain areas, a drought can last for weeks, months, sometimes even years! Forget about running your lawn sprinkler during a drought; the water is needed for drinking, bathing, and toilet flushing.
Another way drought can be used is to refer to a shortage of something (other than rainfall) that lasts for a long period of time, like a drought in job growth during a recession. Typically a drought is not a good thing and something you hope to avoid. For example, if your friend Kenny hasn't gone on a date in five years, it's safe to say that he is having a romantic drought.