Duration is a percentage; DV01 is cash. DV01 = modified duration x price x 0.0001 x face amount. Desks hedge and size in DV01 because it makes different instruments directly comparable: a 2-year note, a 10-year treasury-futures contract and an interest-rate-swap can all be netted once expressed in dollars per basis point.
Risk limits are usually written in DV01 too. A trader might be allowed $50,000 of DV01, meaning a 10 basis point move can cost half a million.
Example: $10,000,000 face of a bond priced at 99, modified duration 7.8. DV01 = 7.8 x 0.99 x 0.0001 x $10,000,000 = $7,722 per basis point. A 15 bp selloff costs $115,830.
Related: modified-duration, basis-point, treasury-futures, duration