Stagflation is a nasty mix of rising prices (based on high demand, production capacity constraints, or both) and falling growth.
When the level of prices in an economy is rising measured by an index such as the retail or consumer price index you have inflation. Usually this is associated with growth as firms become more confident about the price they can charge for goods and services and consumers get wealthier on the back of rising wages.
Equally, when prices are falling, you get deflation. This is often associated with a struggling economy, such as Japan's for much of the last two decades.
Stagflation, on the other hand, is a nasty mix of rising prices (based on high demand, production capacity constraints, or both) and falling growth. It presents a difficult challenge for central banks. Do they raise interest rates to combat inflation, or leave them artificially low to try and encourage growth?