What does the expression count? Let $q \geq 2$.  What does the expression $(q^n-1)(q^n-q)(q^n-q^2)(q^n-q^3)\ldots(q^n-q^{n-1})/n!$ count?  If $q$ is a prime power, then this is
the number of bases of an $n$-dimensional vector space over a field with $q$ elements.
 A: This is a partial answer...perhaps someone will improve on it!  
Historically, most of the $q$-analog formulae (beginning from Euler) were derived based on the assumption that  $|q|< 1$ (to ensure series convergence) or $q=p^k$ for a prime $p$.   John Baez in one of his weekly finds (week184) discusses the geometric interpretation of $q=1$ (counting over $\mathbb CP^n$), $q=-1$ (counting over $\mathbb RP^n$) and $q=$a prime power (counting over PG($\mathbb F_q$)).  There is no discussion for other values of $q$.
However, in Gasper and Rahman's Basic Hypergeometric Series, there is an inversion identity on page 4 which can be used when $|q| > 1$:  

$(a; q)_n = (a^{-1}; p)_n (-a)^n p^{-n(n-1)/2} $ where $p=1/q$.

This returns a new expression in base $|1/q| < 1$.   You can see some examples of the identity being applied in Gasper's Lecture Notes on q-series (Exercise 1.1, Exercise 2.3, pg 14)
I have no idea how to interpret the result geometrically.  Could it be relevant to Buildings, Buekenhout geometry or $p$-adic geometry? 
