In layman's terms (and I consider myself a layman), cognitive delay might best be described as extreme immaturity.
This 16 year old girl may have been functioning as though she was half her age.
On a scale of mental impairment, this is not as severe as mental retardation, but it is approaching it.
Imagine a 16 year old girl cutting out paper dolls and playing with Play-Doh. Perfectly acceptable childhood behavior, but out of sync with her age.
This type of delay is also evident in academics. This 16 year old may be able to comprehend and do basic operations with fractions, but be baffled by grade level mathematics. By contrast, a mentally retarded child would probably be unable to do even that.
One thing as a teacher I've never understood... if there is a "delay" does the child ever catch up? Not that I've seen, but certainly they are capable of working and earning a living.