The answer to this question, in economic terms, comes down to supply and demand. To economists, you can not speak about the price of anything (in this case Oprah's services) without referring to supply and demand.
Presumably, Oprah is able to do something that very few other people can do. In her case, that is to run a talk show that will attract a large audience of people that advertisers want to reach.
If just anyone could do that, the price of that kind of service would be low. But because very few can do it, the supply of such people is said to be low.
When the supply of a good or service is low, its price is high.
This is a simple question of economics. According to many reports, Oprah Winfrey makes around $250 million dollars per year. I was not able to locate any record of how much of that came from salary versus investments, but needless to say she is paid very well.
On the other hand, she brings in revenue to the ABC network. Because so many people watch her show, advertising time is extremely valuable for those who can pay for it. Though I couldn't find exact numbers, the idea would be that ABC would bring in more from the advertising revenues than it pays Oprah to host the show. This is probably the case, but it is also possible that the show breaks even or even a little bit behind.
How does that make economic sense? Well, Oprah is very popular and brings a certain amount of "prestige" to the network she is on. Her name, in connection with ABC, might be more valuable than even the commercial time sold during the show.
So there you go. Economics. Oprah brings in more (either in prestige or ad revenue) than goes out.