The second way to think of them is in terms of different conceptual dimensions as in the first dimension, the second dimension, the third dimension etc. Then there is the even more conceptual way of considering them as different worlds.
If in a dream you are seeing random dimensions of certain objects then this means that you have an odd relationship with objects and all that you see around you. You are thinking very carefully about the things that are presented to you and as a whole you have been pretty analytical overall these past few months or weeks.
If you have a dream in which you see multiple dimensions in the other sense of the word then this means that you are thinking about the consequences of your actions and how you could have changed things that you’ve done in the past, and how changing those things could have affected the future in any number of ways. This line of thought, while endlessly intriguing, is ultimately unhealthy and should be stopped before it does you any more damage.
A dream in which you are trying to find the dimensions of something means that you are trying to look at something in your life through every angle possible. You are trying to interpret something that has happened to you through many different modes and find a way to work past it or work through it.