The network configuration is pretty simple. It might look something like this:
Now that means you could have even more interesting web applications such as a web desktop. Some with a tablet could still generate documents without having any special applications on the tablet. You even set up many other applications without having to use the web. (http://www.instructables.com/id/Uses-for-your-own-private-cloud/)
So now you have double the pleasure. But what if your internet was cut off or you needed to limit your bandwidth. The the network might look something like this, but you would still have access to your local server. This is sometimes known as an intranet.
Sometimes this is called redundancy. You can actually duplicate sites (where allowed by law) from the net on your own systems. With what is called virtual hosts, you can have multiple completely different web sites on your local server. For example:
Really neat possibilities! One thing, I might also mention is that a lot of companies want you to put their web application on your phone or tablet. It means they truly do not understand the "cloud" concept. Those applications waste space and lessens the control and security over your devices and it's installed applications. Real web designers know how to do craft pages that will work with your tablets and phones without you having to download anything. This makes your local server so much more valuable. Also too, web server generally works just fine on older equipment. So there may be no reason to chunk that old computer.
Yes, it is a web server! To tie everything in, you can use a web applications many, times on many machines but only have to install and update it once as the need arises, Have fun!