When you have a website, you will usually have a donate button that allows visitors the chance to click it to go to your donation page. Whether your website is hosted by BlueUtopia or elsewhere, your Blueutopia donation page lives (is hosted on) a completely different web server with a slightly different URL.
So, when a user clicks that donate link/button on your site, they will be taken from your website to your custom-branded donation page. For instance, if your website is at janedoeformayor.com, your donation page might be at secure.blueutopia.com/janedoeformayor/
The donation page will have the same look and feel as your regular website. It does this by incorporating your standard logo and replicating your color-scheme. To the user, it will appear to be a seamless experience.