Use the React Router v4 Link Component for Navigation Between Routes

Can you give a real-world example for when replace would be used in navigation?

There are many situations where it could be useful. Perhaps you have a nested navigation where you want the browser's back button to return to the previous parent url. -- maybe in a modal, or an image gallery... lot's of possibilities.

Do the corresponding Links and Routes need to be in the same lexical scope? Example:

//index.js
import App from './App'
import Signin from './Signin'
...
<Router>
  <div>
    <Route path='/' component={App}></Route>
    <Route path='/signin' component={Signin}/>
  </div>      
</Router>

//App.js
Import Header from './Header.js'
...
<div>
	<Header/>
</div>
...

//Header.js
<nav>
    <ul>
        <Link to='/signin'>Sign in</Link>
    </ul>
</nav>

I had tried making a route change to the route /signin from a nested component, and although it would go to the route within the "to" parameter, it wouldn't render the component until I refreshed the page. Does anyone know if this is an issue or a feature?

Without a detailed review of your code it could be multiple issues. However, as you've presented it here App & Signin should both render at /signin. As just a random thing to try - <Route exact path='/' component={App}></Route> to see if the two components are conflicting somehow.

Is it possible to have several routes on one page, like in a single scrolling webpage that has each section take up 100vh of the users window?