The IRR represents the actual return of an investment over an arbitrary
period of time (usually annualized).
Say, for example, that you invest $100 and, after two years, you have
$120. Your overall return is 20%. If your interest rate was constant
over the two-year period and you never took any money out or put any
money in, your annualized IRR, that is the percentage that best
approximates how much you've made on a yearly basis, is approximately
9.544% and is calculated through the simple formula
IRR = (EndAmount / StartAmount) ^ (1 / NumberofPeriods) - 1.
IRR = (120 / 100) ^ (1 / 2) - 1 =~ 0.95445
If it sounds like a straightforward calculation... it isn't, because you
rarely have a clean-cut situation like that. Most of the time, you have
to deal with variations in the cash flows (interest payments,
reinvestments, disbursements, taxes, and so forth) and partial periods.
In some cases, the problem can only be solved by interpolation and the
calculation can become quite complex.