As far as english speaking people are concerned, this is spoken by snooty types as to sound more sophisticated than they are, used humorously as such by people who *do* know what it means, and spoken by French when they need to say "I don't know what" in French.
Generally speaking, can be used if you're feeling particularly suave to give an explanation of something of a certain unknown or indescribable quality.
See also unobtanium.
This French idiom is frowned upon by people who feel socially, economically, or mentally threatened because they can't stand "snobs" who use this phrase (see first definition in this list). People who fear foreign languages also have a tendency to have small reproductive organs, carry big guys to compensate for their lack of confidence, and are generally socially inept when trying to carry on an intelligent conversation with people smarter then them.
"I don't know about that guy over there, there's definitely no je ne sais quoi in his life."
"That poor unintelligent bastard over there doesn't like people who say je ne sais quoi."