The full meaning is:
"Have no worries about it" --->>> "No worries" (I believe "no worries" is primarily of Australian origin)
"It's not a thing you should worry about --->>> "It's no worry"
also: "Not to worry"
"no worries" is nicest, I'm American, and many of us do say this nowadays, but we haven't imported "g'day" from the Australians yet.
it's kind of like "Gracias" (spanish for "thanks"), it's a word which wasn't really used in USA, but everyone knows it and we integrated it into our vernacular.