You can use it when you want to say "my absolute recommendation". For example: You will receive my wholehearted endorsement if you run for president.

"Endorsement" can mean "recommendation" or "approval." When an athlete appears in an advertisement for running shoes and says "These running shoes are great!" he is endorsing the shoes. When there is an election, and, let's say, a labor union says "We endorse candidate X," it means they think candidate X is best and are recommending that union members vote for X. "Wholehearted" means completely, fully, sincerely. It strengthens the feeling. "X has my endorsement" means "I recommend X." "X has my wholehearted endorsement" means "I recommend X highly."