picker.delegate = self;

A bit more context possible ? where did you saw that line ?

Let's assume in this context ...

https://developer.apple.com/library..._Protocol/Reference/UIPickerViewDelegate.html

The protocol just define the methods and is not a class definition whch can be used to initiate an instance. The protocol need to be referenced and implemented by a delegation class (could be a view controller).

Set the delegate is required so that the instance which implement the protocol (like "callback" methods) for the picker actually can be addressed.