Site is banned

What is ban?
When your site gets excluded from the index of a search engine - that is ban.

How does one know if his site is banned?
Simply.
Type site:mysite.com query in the Google search box, where mysite.com is the URL of your site.
If you don't see any results then - congratulations, your site is either banned, or has never been crawled (true for brand new sites).

Why would Google ban a site?
Mostly, because that site violates Google Webmaster Guidelines or uses blackhat SEO methods.

How can one bring the site back to Google index?
Step one: remove all blackhat stuff from your website.
Step two: submit your site to Google again.