Hyperinflation is when a rate of inflation grows exponentially, and a currency is rapidly devalued. Hyperinflation occurs in the midst of dire economic circumstances.
This is usually partially due to the piling on of downward price pressure in which newly printed currency rapidly floods the market as the government attempts to cover debt obligations. Sometimes this stems from situations where the government is having trouble receiving adequate taxes from the population.
When a currency is rapidly inflating, people will seek to exchange it for physical goods or foreign currencies as quickly as possible, which increases the Velocity of Money and adds to the inflation. There are many examples of hyperinflation, going back to ancient Egypt and plenty more in the modern era.