What does the g-factor, from say ESR, tell you?

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From ESR data you can extract the g-factor and "effective" magnetic field. Let's say I get this g-factor from ESR, what does it tell me? i.e. "if the g-factor is X then Y is happening in the system". What specific information can I get from knowing this factor? What causes it to differ from 2.0003.. whatever?
 
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atyy said:
I googled and found http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Paramagnetic_Resonance/EPR:_Interpretation.

"The magnetic field for resonance is not a unique “fingerprint” for the identification of a compound because spectra can be acquired at different microwave frequencies. Then what is the fingerprint of a molecule? It is Δg."

Right but this is the trivial case. Like when biologists use it to identify free radicals in solution. I'm talking about thing like in Condensed Matter, where you already know what the substance is but people do ESR to tell you... something. I understand that the splitting of peaks can help you identify hyperfine splitting and thus the relative influence of nearby ionics cores on the free electron but what does the g-factor tell you?
 
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