What it means
The elephant and the lion. That is the picture behind the name Gaja Kesari. A person with this yoga is said to carry quiet authority. People defer to them and rarely know why.
The classic test is Jupiter in a kendra (1st, 4th, 7th or 10th house) counted from the Moon, not from the Lagna. That placement alone appears in about a third of charts, so by itself it proves little. Many readers add two safety checks. Jupiter should not be debilitated, and it should not be combust, which means too close to the Sun to give its light.
This rule runs all three. The two safety checks remove roughly one match in ten. That sounds small, but the charts they remove are the ones the texts call weak.
Traditionally the yoga gives a good name, a steady reputation and the goodwill of elders. It does not give wealth by itself. Check yours, then think about who treats you as the senior person in the room.
The rule uses the Moon as the starting point. Open it to see how the builder counts houses from a planet.