I would like to know how throw works in PHP.
For example, does it act like a die() or exit()? How can I know what is done internally?
I am asking this because I saw Kohana using their $this->redirect() method with a throw to terminate the script execution instead of the traditional exit.
As already explained, you use throw to throw exceptions that can be caught "further up" in your application.
When you work with objects and object oriented programming you start coding every single object you make as a standalone object that you can give to someone else. The public methods of these are an API, and the phpdoc above each public method details what exceptions the class might throw under certain circumstances.
So, someone has created a standalone object that does something for you, like writing to a disk. You want to use this object, so you look at the docs and see it throws a PermissionsException when the object can't write to the disk because of a permissions issue.
In your code that uses this person's object, you now know that you should catch that exception, log it, and continue however you want your application to work given that circumstance (show a nice error to the user if it's via an AJAX call, for example).
So, knowing this, when you code your own objects, make descriptive exceptions for different circumstances that someone who you give your object to can use and respond to in their own applications.
Both die and exit you don't really want to use in production applications. They're useful for debugging when you do a var_dump() and then want to halt application execution straight afterwards or if you want to completely stop the script from running for some reason.
As for why your specific found piece of code does it this way, you should ask the developer if it isn't documented with good reasoning.