In a baroclinic fluid, the thermal-wind balance holds, which is a combination of the geostrophic balance and the hydrostatic balance. This implies that isopycnals can slope with respect to the isobars. Furthermore, this also results in changing horizontal velocities with height as a result of horizontal temperature and therefore density gradients.
Under the thermal-wind balance, geostrophic balance and hydrostatic balance, a flow is in equilibrium. However, this is not the equilibrium of least energy.  A reduction in slope of the isopycnals would lower the center of gravity and therefore also the potential energy. It would also reduce the pressure gradient, leading to an increase in the kinetic energy. However, under the thermal-wind balance, a decrease in slope of the isopycnals cannot occur spontaneously. It requires a change of potential vorticity.  Under certain conditions, slight perturbations of the equilibrium under the thermal-wind balance may increase, leading to larger perturbations from the initial state and thus the growth of an instability. 
It is often considered that baroclinic instability is the mechanism which extracts potential energy stored in horizontal density gradients and uses this "eddy potential energy" to drive eddies.