Location
Our Milky Way galaxy is orbited by a satellite galaxy called the Large Magellanic Cloud (LMC). Inside that galaxy is a region called the "large super bubble" or LMC-4. Inside that region is a region called LMC N 63. Inside that region is a supernova LMC N 63A.
What Exploded
The former star is believed to have exploded 2000 to 5000 years ago. It is projected that the former star was 50 times more massive than our Sun. Here's a theory on what happened before the explosion... Such massive stars, as this star is believed to have been, have strong intersellar winds that can form a wind-blowing bubble. This wind-blowing bubble had a central cavity where the star exploded.
Sources:
http://hubblesite.org/newscenter/archive/releases/2005/15/
Image soure NASA