It sounds like you got it basically right, but now think about the sentence "the universe is a part of our dimension" which would mean "the universe is a part of our universe".
The scifi "dimension" is as meaningless as "plane of existence"; it just sounds nice when you want to explain things away in scifi. I mean, it seems to be easier in scifi to travel between those "dimensions" than between the Milky Way and any other galaxy in the visible universe.