WordPress runs on any computer but it requires a web server with PHP and MySQL. MySQL is database that holds the settings, posts, pages and all other content stuff. PHP is the code, language that WordPress was built on and web server simply something that runs everything else tied in.
Now you don’t really need a hosting to install WordPress, you can use application like MAMP to install and run WordPress on your local computer. MAMP is a kit that with one install installs apache, php and MySQL on your computer so you can run WordPress.
Now there is three major choices, two of them are slightly complicated but they will make your WordPress website live on the internet, while one of the three will only be available and viewable by you only.
Option #1; get hosting and install WordPress there, get also a domain.
Option #2; install MAMP on your computer, setup domain name, get a service like NoIP so you can tie in your dynamic IP address (because it constantly changes by your isp) to your domain and do port forwarding to the right port, etc… On your computer. After proper setup, your website will be live as long as your computer is live and everything runs on your home computer, not some hosting company.
Option #3; run MAMP with WordPress, just like option above but without NoIP service and using no domain. This way, going to localhost in your web browser will show you your WordPress website but because it’s local, you are only able to see it from home and no one else outside your home.
So many different options to install and run your website. If its just a simple local home test type installation you are looking for; grab a copy of MAMP, install, download WordPress, copy to directory MAMP defined as web server directory, setup a database and go through the WordPress install.
Hope that gives a light on how to go about an install ?? thank you.