It's possible to install WordPress on your local computer, but you'll need to set up a "server environment" on your computer in order for it to work. Here's some good information about WP and that kind of installation. But do be aware that if you start out with it on your local computer, you will then have to move it which can be a bit complicated.
http://codex.wordpress.org/New_To_WordPress_-_Where_to_Start
http://codex.wordpress.org/Installing_WordPress#Installing_WordPress_on_your_own_Computer