High Speed Sync HSS
Most dslr cameras flash will sync up to a shutter speed at around 1/250th second. With HSS you can push this all the way to 1/800th.
When you are out doors in bright sunshine and you want fill flash and shallow depth of field.
When you've accidently left your on high ISO, so basically you can shoot on Av, e.g. you're at a wedding and you've just moved from inside the church to bright sunshine.
Less power as you go faster.