See, you actually need Apache-PHP-MySQL.
Apache is a webserver software. PHP is a language for server-side scripting and Wordpress is programmed using PHP. MySQL is for databases.
If you use windows, you can simply download XAMPP Lite from here - *www.apachefriends.org/en/xampp-windows.html#646 which will automatically install the above three.
Then there will be a folder named 'htdocs' in the location where you've installed XAMPP, you have to save your website files over there.
Like, if you saved a file named 'gfxdev.html' in that htdocs folder, to access it site from your own computer, you just have to open a browser type *localhost/gfxdev.html
I hope you got what I mean.
You can download Wordpress from here,
www.wordpress.org, create a database using *localhost/phpmyadmin (don't worry this will be get installed by default) and configure wordpress accordingly. You'll have an offline installation of Wordpress running on your system.
In this case, I've installed Wordpress in 'htdocs/wordpress' folder and I can access it using *localhost/wordpress
*img411.imageshack.us/img411/7922/screenshotcy.th.jpg