Used in a handicap race, where a horse has to carry a big weight on its back.
The more weight a horse has to carry, the harder they have to work in the run. But it's usually the classier horses that have to carry more weight.
However, when a horse is carrying an elephant, it means that they have too much weight on their back to be a realistic winning chance.
"I know he's the class runner, but he's carrying an elephant with the 62kgs. No chance."