The word "into" means one thing is moved inside of something else.
"Put the candy into the bowl" is a command which means the candy must be placed inside of the bowl.
"Go into the store" is a command, it means you must go inside of the store.
"Look into the mirror" has the same sort of meaning. You are not actually inside the mirror, but your gaze feels like it is going inside.
"An investigation into the massacre" has a similar meaning because when you investigate something it feels like you are going right inside of the problem and looking around.
You could say "the FBI are looking AT the massacre", but "looking at" is a passive expression and it doesn't give the feeling that the FBI is going to do a serious investigation. But if you say "the FBI are looking INTO the massacre", then it sounds a little more serious.