It means having other websites link back to you.
For example, Look at my signature.
It has links embedded in some text..
So "Live chat support" or "Live support chat" will link to
www.imsupporting.com
Google *May pick up on these links back to my site.
It would then decide based on who has linked back to you and how many sites have linked back to you just how important your site is.
Depending on the outcome of googles results your page may appear higher with more backlinks to your site.
Its a way that google and some other engines check just how popular or reliable your site is based on keywords and content.
Google was first called "backrub" IE: checking backlinks to sites and baseing the results on how many links there are.
Google has moved on from this now, So backlinks alone only hold some weight in the results.
Other factors some known and some unknown come into play.
basically, the more backlinks to your site th ebetter. However dont waste your time and money just checking these and doing them.
Backlinks will come naturally if you have a good site.