Cook admits that Apple could have built its own subscription service and headphones, but he sees Beats as offering far more than that thanks to "incredible" and "creative" people — particularly Iovine and Dre.
I think this is the primary reason they bought Beats. Apple has steadily been loosing "street cred" in the music industry. Most labels see Apple as a thread now-a-days and provide better deals to their competitors like Amazon and Google. By bringing two major record industry figures under the Apple umbrella, they can try and rebuild trust with the music industry.