For me, the positions are like extensions of the sig, reflecting the body.
1) situation--where you're at, heart of the matter
2) cross--hurdle or bridge, or what holds the situation in place
3) beneath--where you stand (or sit) (root, unconscious)
4) crown--where your head's at (conscious)--thoughts or aspirations
5) behind--receding influence, or something to move away from
6) before--what you're facing, or something to move toward
So the vertical is, IMO, all about you, whereas the horizontal can be internal or external factors . . . as can the next two cards. And I think positions 7 and 8, more than any other, depend on previous cards.
7) self--either internally or externally (reality or presentation)
8) extern--some say that this can be either outside influences, or how you appear to others. Of course, how others perceive you affects how they interact with you, so that would actually be a "sub-influence."
9) psyche--subconscious, either how it affects the situation, or what it needs from the situation (a.k.a. "guidance")
10) outcome --can't say it any better than that
I frequently use an adaptation, placing cards 7 through 10 x-wise, in the four corners of the previous cards, rather than in a line to the side. This subtly alters the meanings of these cards. Have a look at this Celtic Square spread.
Joan Bunning has a great section on Celtic Cross and its positions on her web site.