Variable Rate Demand Obligation. Translation: a redeemable debt that has a changing interest rate.
Example
You have a variable rate bond. It adjusts annually and it pays 100 basis points above LIBOR. This particular bond, however, has a demand obligation which makes it automatically convertible into a flat 7% yield bond, payable in U.S. dollars, if the dollar to Euro ratio ever drops below 1:1. The bond carries this VRDO feature as a kind of hedge against strange fluctuations in currencies, interest rates, and other bizarroland occurrences.