Private IP/non-routable address?

What does this mean? I found a web address saved in s/o's history with a password but the web address is literally just numbers

Http://172.24.108.48:10080

It seems impossible to figure out wtf this means because all browsers block it.

I read it's called a private/non-routable address but what does that mean and why would someone use it?

I'm relatively illiterate when it comes to this kind of thing but I have a very bad feeling about it.