“Speak volumes” means to reveal a lot of information. We usually use it when action (or lack of action) shows a fact very clearly -often without needing words. So the rich person’s donations reveal the fact that they are truly very generous.
People often say that an action, a lack of action, a picture, or a facial expression speaks volumes. If the government says that education is important, but doesn’t invest any funds or resources in education, that speaks volumes about their true priorities -it clearly shows that they actually DON’T consider education important. If you cook a dish for your friend and it doesn’t taste good, your friend might not say anything directly… but the disgusted expression on their face would speak volumes -it would reveal the fact that they didn’t like the food.