From their FAQ:
The Opera group consists of Opera Software ASA, maker of the Opera browsers; Opera Mediaworks, the world's largest mobile advertising platform (including AdMarvel, an ad-serving and mediation platform; Mobile Theory, a premium mobile ad network in the United States; 4th Screen Advertising Ltd., a premium ad network in the United Kingdom; and Opera Mediaworks Performance, a results-driven mobile ad network); and Skyfire Labs, who improves the mobile internet experience by using cloud computing.
Most of their income comes from these ads networks and related services. The browser is their flagship product and the 'face' of the company but the money is in their ads.