The billionaire owns 3.9 million shares of Apple worth about $2 billion, and he also owns 16.9% of Nuance. A purchase of Nuance by Apple would have to be done at a premium to the current stock price, which would probably result in huge profits for Icahn. Nuance is known for its Dragon voice recognition software and in 2011 the company purchased swipe to type firm Swype for $100 million.
But right now, Icahn is not pushing Apple CEO Tim Cook to buy Nuance. What he is pushing Cook to do is borrow $150 billion at 3% interest and use the funds to buy back $150 billion of Apple shares. That would retire the stock, raise the earnings per share, and according to Icahn, raise the price of Apple's stock by 33%.
So far, Apple has resisted the pressure from the investor, but don't expect him to give up easily. That is Icahn's usual game plan. He buys a huge position in a company he considers undervalued and cajoles the CEO into buying back stock or taking other actions that would bring the price of the stock up and allow the former options whiz to reap a huge profit.