  The microscopic origin of the $\gamma$-softness (fluctuations in the
triaxiality parameter $\gamma$ of the nuclear shape) observed in atomic nuclei
is studied in the framework of the triaxial projected shell model approach,
which is based on the deformed mean-field picture with multi-quasiparticle
configuration space. It is demonstrated that the coupling to quasiparticle
excitations drives the system from a $\gamma$-rigid to a $\gamma$-soft pattern.
As an illustrative example for a $\gamma$-soft nucleus, a detailed study has
been performed for the $^{104}$Ru nucleus. The experimental energies and a
large sample of measured $E2$ matrix elements available for this nucleus are
reproduced quite accurately. The shape invariant analysis of the calculated
$E2$ matrix elements elucidates the $\gamma$-soft nature of $^{104}$Ru.
