This is method level dependency injection. The Request is being passed into the store method, instead of the store method knowing how to create the Request object.
The type hint in the method signature does two things.
First, for plain PHP, it enforces the fact that the parameter passed to the store method must be a Request object, or an object that inherits from Request. If you attempt to call the store() method with anything other than a Request object (or descendant), you will get an error.
Because of this strict type enforcement, we know that the $request parameter must be a Request object (or descendant), and we can depend on its public interface being available for use (you know the input() method will exist).
Second, for Laravel, it tells the Laravel container what type of object this method needs, so that the correct object can be resolved out of the container and passed to the method. Laravel's controller methods are called through the container, which allows automatic dependency resolution of method calls.
If you were to remove the type hint, this would cause two issues. At an abstract level, it would allow you to pass any type of object, or even scalar values, to the store() method. If you attempt to call input() on a string, you're going to have problems. At a more concrete level, this will break Laravel's automatic dependency resolution of controller methods. Without the type hint, Laravel can't know what object the method requires, so it won't pass in anything, so in reality you'd get an error saying that you can't call input() on null (or an error saying the store method requires one parameter; not sure, didn't test).