Well, without further context, it's hard to say precisely. It might be that 'he' is a friend, a salesman, or even a relative. If he's a friend, perhaps he convinced your wife to join a club or take up a new hobby. If it's a salesman, he could've convinced her to purchase a product she wasn't initially interested in.
Since we don't have much information, there are numerous possibilities. It could be a story where 'he' convinced your wife to support a local cause. He might have presented such a compelling argument that she was swayed. Or it could be something more personal, like he convinced her to forgive someone. We really need more details to know for sure.