The rate at which the overall price level in an economy increases. Inflation causes a decrease in the purchasing power of money.
Suppose the annual inflation rate of an economy is 5%. That means, on average a product (e.g. a shirt) that costs 10 $ this year, will cost 10.50 $ next year. As a result, the amount of goods you can buy with 10 $ decreases, thus purchasing power falls.
Changes in price levels and purchasing power have significant implications for overall wealth and wealth distribution in an economy. A moderate level of inflation is generally accepted and taken as a sign of a growing economy. However if inflation is too high, people will eventually lose faith in the currency and the economy.