.. should have added that if you want your home page to look less like a blog and more like a normal web site, you just create what you want as a page and set that as the home page from the Dashboard in Settings -> Reading (the term 'static page' is used here rather than just 'page' - WordPress is a bit inconsistent sometimes).
There are two sites: wordpress.com (which is what you have signed up to use) and wordpress.org where you can download software that is basically the same as that used on wordpress.com so that you can upload it to whatever web hosting service you want.
The former is suitable for beginners although some larger businesses use it too, the latter is suitable for people who want or need more control over their web site and are prepared to put in the time keeping it running properly.
You make web sites (with either flavour of WordPress) by creating pages from the dashboard.
I've read that you can make nice websites with wordpress even though it is mainly a blogging platform. I'm part of a blog with it (new) and edit/use it online, so why when I search online for it i get a message to download it? How do you make websites with it? very .