Up-down, back and forth and in and out.

Get your mind out of the gutter. It's not what you think.
I finally figured out a way to think of the extra dimensions and what they mean. Forgetting the time dimension there are three dimensions with which we are familiar (Up-down, back and forth and in and out). That just means that any object is free to move in each of the three directions (dimensions). My realization came when I realized that 'other objects' could be moving in the extra dimensions. The 'other objects' could simply be other attributes of space. Spin and quantum number are two that spring to mind. Each of the attributes are free to move in its extra dimension. Mathematically it turns out that 7 attributes inhabiting 7 extra dimensions avoids the disastrous infinities associated with more or fewer than 10 dimensions (3+7+time).
That would also explain why we cannot travel from one space dimension to another dimension of spin, which is already occupied.
Or not.
Travelling through extra dimensions is proof that we're all on this flight together.

Dick