To add on to the above, which is all correct, it also appears the site you mention has a custom designed theme.
A WordPress site consists of the same base code, and then you add a theme (design) and plugins (functionality) that you like. All of this is hosted on a server which is what Pioneer linked to above, or you can read more on the “Hosting” link above (in the black menu) to learn a little more about hosting as well. You can also see what themes and plugins are freely available in those sections of this site.
If what you want to do does not exist, you can hire someone to create it for you. One such way is to hire a WordPress company through jobs.wordpress.net or just search online for someone or ask someone who has been helpful in the forums if they do customized work.
If you are just getting started I’d say sign up for a free blog at https://www.wordpress.com and “play around a bit” and see what you come up with. That will give you a better idea of if you want to go for it on your own or hire a partner.
