Any hyperlink that is linking to a web page on your website from external web page is called a backlink.
In English, any link from another website with a different domain (hisdomain.com) to a web page on your site (yourdomain.com) is called a backlink. The backlink could be from entierly different domain, or it could be a web page in your sub-domain.
How do you check your backlinks?
There are many paid and free tools in the market that you can use to find out who is linking to you. I will just suggest a few FREE ones I most oftenly use for your reference.
Google Webmaster tools
Google Webmaster Tools shows backlinks on your sites that Google can find on their indexed pages, but for some reason it did not display the backlinks when captured the screen ... server error?