Your web presence typically consists of a normal web site and a mobile site. There may be many more types of sites in future and Jmbo Foundry makes it easy to configure them independently. If your main site is served on www.mysite.com then go to Sites in the admin interface and set Domain name and Display name accordingly. Then add a site entry for your mobile site and set the values to m.mysite.com.
If you have only one site then you may blindly publish everything that is publishable to this site. However, if you have more than one site and in different languages then understanding sites become significant.
At its most basic level publishing to a site means making content appear on a site. This is easy to understand when the content is eg. an article, but content is not always limited to things which are easily translatable into real world objects.