Difference between protocol and delegates?

A protocol, declared with the (@protocol syntax in Objective-C) is used to declare a set of methods that a class "adopts" (declares that it will use this protocol) will implement. This means that you can specify in your code that, "you don't care which class is used as long as it implements a particular protocol". This can be done in Objective-C as follows:
id<MyProtocol> instanceOfClassThatImplementsMyProtocol;
If you state this in your code, then any class that "conforms" to the protocol MyProtocol can be used in the variable instanceOfClassThatImplementsMyProtocol. This means that the code that uses this variable knows that it can use whichever methods are defined in MyProtocol with this particular variable, regardless of what class it is. This is a great way of avoiding the inheritance design pattern, and avoids tight coupling.
Delegates are a use of the language feature of protocols. The delegation design pattern is a way of designing your code to use protocols where necessary. In the Cocoa frameworks, the delegate design pattern is used to specify an instance of a class which conforms to a particular protocol. This particular protocol specifies methods that the delegate class should implement to perform specific actions at given events. The class that uses the delegate knows that its delegate coforms to the protocol, so it knows that it can call the implemented methods at given times. This design pattern is a great way of decoupling the classes, because it makes it really easy to exchange one delegate instance for another - all the programmer has to do is ensure that the replacement instance or class conforms to the necessary protocol (i.e. it implements the methods specified in the protocol)!
Protocols and delegates are not restricted only to Objective-C and Mac/iOS development, but the Objective-C language and the Apple frameworks make heavy use of this awesome language feature and design pattern.

Introduction

Protocols can be helpful in a number of scenarios, a common usage is to define methods that are to be implemented by other classes. A familiar example is when using a tableview, your class implements the cellForRowAtIndexPath method which asks for cell content to insert into a table – the cellForRowAtIndexPath method is defined within the UITableViewDataSource protocol.

Protocols are like contracts, Your class must implement all methods that are @required, @optional are on the other hand not required.

Instead of Protocols why can't I make my classes do the same job? You can, but like I wrote above, its a contract. You know that class

implements the (Required) methods.
delegate is (should be) a weak reference to the class that implements the given protocol.
You are recommended to use the following attribute on your delegateproperty:

@property (assign) id<yourProtocol> delegate;

Notice that you don't retain your delegate. You you (weak) reference because you dont want to get into a retain circle (A retains B, and B retains A).
I hope my explanation helped a bit.