Why do people say “no offense” when starting a sentence?

English is my second language and I mainly learn it from shows like modern family and the bigbang theory.

I know what “no offense” means, but I don’t think I fully understand its usage. I’ve seen many people saying it before they say something insulting. But does including “no offense” make the statement less offensive? I don’t really get why people use it...

Solution 1:

"No offense" is short for "No offense intended." I'm adding this answer because it wasn't explicitly stated in the comments and someone reading the question might not get the full idea: It means "I'm going to speak bluntly but don't mean to hurt you by saying it." Even so, as user 888379 indicates, it might not be said sincerely.