Passing arguments/parameters in android

It's well documented here:

public  Intent  (Context  packageContext, Class<?>  cls)
Since: API Level 1

Create an intent for a specific component. All other fields (action, data, type, class) are null, though they can be modified later with explicit calls. This provides a convenient way to create an intent that is intended to execute a hard-coded class name, rather than relying on the system to find an appropriate class for you; see setComponent(ComponentName) for more information on the repercussions of this.
Parameters
packageContext  A Context of the application package implementing this class.
cls     The component class that is to be used for the intent.

The arguments for the Intent in this case would be a Context and a Class.

Context is a fantastically useful piece of the Android system that basically allows the program to keep track of what is displayed and where resources are. In some ways you could consider it like System in other... systems. A lot of things require context in order to ensure that everything is working given its loosely coupled nature.

the Class that's required is the compiled version of your .Java files so to run MainActivity.java you would pass MainActivity.Class

Think of the process of using Intents to start Activities as being analogous to instantiating objects using the Java new keyword. Example...

MyClass.java

public class MyClass {
}

In some other code...

MyClass exampleClass = new MyClass();

In Android Activities are in essence simply just Java classes - they are, however, 'special' classes and as such we don't use new to instantiate them. Instead we ask the Android system to instantiate them for us.

In the example you give, you are defining explicitly which Activity class to instantiate...

MainActivity.java

public class MainActivity extends Activity {
}

Then in some other code you use the following...

Intent intent = new Intent (this, MainActivity.class);
startActivity(intent);

The call to startActivity(...) is the way of asking the Android system to instantiate a 'new' instance of MainActivity.

As has been mentioned in the other posts, this method requires passing an Android Context which in this case is done using this. What that means is the application component which is requesting to create a new instance of MainActivity is passing itself as the Context.