I believe that 'excess burden' is essentially how many more people than expected would show these outcomes. IE, if normally you'd expect to see 5/1000 people in a control group experience a stroke, but observe stokes in 15/1000 people in your non-control group, the excess burden would be 10/1000.

HR appears to be 'hazard ratio' which is simply a ratio between the two groups. The above example would have a hazard ratio of 3, as three times as many people presented with the outcome than expected.