Effective potential allows us to answer the question that whether there will be spontaneous symmetry breaking induced by quantum corrections. Is there any other information that can be extracted from the effective potential and effective action? Does this term has anything to do with effective field theory?
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Related: http://physics.stackexchange.com/q/17689/2451 and links therein. – Qmechanic Mar 17 '16 at 10:29
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The effective in effective action has nothing to do with the effective in effective field theory. An effective field theory is a low-energy theory (described by some action $S_{eff}$ and cut-off $\Lambda_{eff}$) of some given higher energy theory (with action $S$ and cut-off $\Lambda\gg\Lambda_{eff}$).
The effective action $\Gamma$, which is sometimes called the quantum action, is the Legendre transform of the partition function of $S$ in presence of sources. It therefore includes all the energy below $\Lambda$, and is, at least in principle (if you were able to compute it exactly), an exact description of the whole physics of the field theory. From it, you can access all physical quantities you would ever want: vev, propagators, scattering amplitudes, etc.
Of course, if the physics of $S$ is well described by $S_{eff}$ at low energy, then the physics you get from $\Gamma$ at low energy will be equivalent to the physics you would get from $\Gamma_{eff}$, the effective (quantum) action of the effective field theory described by $S_{eff}$.
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