You could read the definition in dozens of dictionaries and encyclopedias like this
http://en.wikipedia.org/wiki/Phenomenology_%28science%29
My feeling is that the term is related to the word "Phenomena" that is something that is observed. Thus, the phenomenological models and equations describe rather instrument readings than some fundamental processes behind it. For example, there is a relaxation time $\alpha$ in quantum physics which is often taken as a constant in the exponential factor $e^{-\alpha t}$ since the experimental results show nearly exponential decay of the non-equilibrium particle concentration. That is the phenomenological approach. Alternative approach is to compute this quantity using fundamental physics and taken into account scattering processes standing behind this exponential decay.
Usually, phenomenological method utilizes a kind of scientific intuition. Soon or later, most phenomenological quantities are proved by theoretical computations if they describe the experimental situation with satisfactory accuracy.
This post imported from StackExchange Physics at 2014-03-07 14:33 (UCT), posted by SE-user freude