Also spelled nosey. The 'nosy' spelling seems to be about three times as popular, as shown by Google searches, but both spellings appear in most dictionaries.
These days nosy means overly curious, especially in reference to a person too interested in gossip and other people's personal lives. It is almost always a negative label.
The word nosey appeared as early as 1620, but only as a way of saying that someone had a big nose. The Duke of Wellington, for example, had the nickname 'Old Nosey'.
If Webster 1913 was here, he would have the more modern definition of nosy. It first appeared in 1882, presumably as a figurative way of saying a person was always sticking their nose into other people's affairs.