When you program for iOS, you take advantage of a suite of frameworks provided by Apple. These frameworks, taken together, constitute Cocoa; the brand of Cocoa that provides the API for programming iOS is Cocoa Touch. Cocoa thus plays an important and fundamental role in iOS programming; your code will ultimately be almost entirely about communicating with Cocoa — interacting with the frameworks provided by Apple, in order to make an app that does what you want it to do.
The Cocoa Touch frameworks are a huge boon to you, the programmer, because they provide the underlying functionality that any iOS app needs to have. Your app can put up a window, show the interface containing a button, respond to that button being tapped by the user, and so forth, because Cocoa knows how to do those things. But with the great advantages of working with a framework come great responsibilities. You have to think the way the framework thinks, put your code where the framework expects it, and fulfill many obligations imposed on you by the framework.