At the end of all the virtual DOM it is going to call the browser API to update the real DOM then how come it will be faster?
Any speed benefits come from minimizing the number of DOM manipulations that are needed and doing them all at once. The virtual DOM is react's way of calculating the minimum set of changes.
Here's what i mean by calculating the minimum set of changes: The page starts off looking one way, and then you want to make it look some other way. To get there, you're going to need to make one or more changes to the DOM, but there are many different ways you could do it.
A really bad way to update the page would be to wipe the entire document, and then rebuild every single element from scratch. Most likely though, you can reuse most of the page and just make a few updates to select parts of the page: add a div here; update a property there, add an event listener there. That's what you want: a small number of steps that take the old page and turn it into the new page.