Vector means that instead of every pixel saved in memory, there are only instructions how did maker of the room made it. Like in some programming languages: Circle (1,1,10,10). (Of course it isn't written with words.)
It saves room, because: for example we would want to make line from coordinates 0,0 to coordinates 20,20. In raster graphics you should store 200 bytes (every pixel with colors), but when making it in vector we only should use 6 bytes.
And AGI pictures do not have an single extension, when they are in AGI game, then they are in resource file(s) with picdir to show where they are. When they are extracted, they are usually named like picture.001 and so on.