The going describes the condition of the course - the state of the ground.
Heavy going makes for tiring work
All horses are built differently and have varying "actions" (styles of running).
Horses that gallop with a high, rounded action often prefer running on softer ground as their legs are hitting the ground from a greater height than horses with a flatter action.
In Britain, there are seven official going descriptions: hard, firm, good to firm, good, good to soft, soft, heavy.
Although softer ground is more tiring which means horses are more likely to fall, injuries tend to be less serious because the ground provides a cushioning effect for those fallers.