In finance, duration - strictly defined - is the weighted average timing of all of an instrument’s cashflows, where the weightings are the present values of the cashflows at the current market yield. By formula, Duration = Sum(PVt)/Sum(PV).
Duration is widely used as a risk measure of a portfolio of assets or liabilities. It gives a general indication of the sensitivity of an instrument's or a portfolio's market price to small changes in market yield. (Modified duration measures this in a more refined way.)
Broadly speaking, the longer the duration, the more sensitive the market price is likely to be to (small) changes in interest rates. Duration is also used as a measure to compare debt securities that have different maturities and yields.
More strictly, the duration of an instrument specifies the remaining life of a zero coupon bond with the same value sensitivity (to a very small change in yield). Both can be regarded as equivalent to a single future cash flow after this period of time. If there is uncertainty about the timing or the occurrence of future cashflows - for example a call option on a bond - then the concept and calculation of duration becomes more complex.
Not to be confused with maturity, which is different.
More loosely, the terms duration and Modified duration are often used interchangeably.
Obviously this can lead to potential confusion, so it is important to clarify whether duration or modified duration is intended in any particular context.