Civil contempt can be generally viewed as (not) doing something for the benefit of the complainant. In criminal contempt it's for the benefit (or protection of the sanctity) of the court itself.

The most common reason for holding someone in contempt is for refusing to follow an order to pay money. Ordering them to pay more money isn't going to be effective. There really isn't anything else you can do. You can take their stuff, but if they had assets that could easily be seized, you would do that in the first place.

Corporations can be fined into compliance because making money is generally a corporation's only purpose. The closest equivalent for and individual is removing time from their life--jail time.

A jail cell is basically the last resort to force compliance. It's also what will eventually happen to individuals running a corporation if they keep defying court orders.