How does the service delete todo method actually remove the element from the HTML?

In this video ( https://teamtreehouse.com/library/using-services-to-save-and-delete-data ) he creates a new method in the service and passes it into the controller. I understand how this works, but what I don't understand is how exactly the HTML element is removed from the web page when he clicks delete.

What I do understand is how the method is attached to the service then passed to the controller.

I do understand how he grabs the index from the todo array and how he uses the index in the function to splice (remove) the todo from the array.

What I don't get is how the HTML is updated just because a variable is deleted. I would think that you would also have to include some event listener to see when a "change" is made or something and then update the live html in the browser.