Meaning of coupling factor for a resonance cavity
Resonant Coupling Factor relates the mutual coupling two resonators (e.g. LC type) with tunable "crosstalk capacitance" or "mutual inductance"  such that the overall bandwidth is increased by spreading the high Q centre frequencies apart to obtain steep skirts yet low ripple in the passband.  


A double-humped response indicates overcoupling,
critically coupled reduces the peaks on either side and the centre valley to meet the desired passband, PB ripple spec near 0 dB  (see Reference)



Below shown with a Capacitive Transformer (or C ratio) instead of inductive transformer as in question. But same effects. Here the C ratio =1.


Note: The crosstalk C = 0.1pF is really tiny and must be well-shielded.



For further reading 

https://en.wikipedia.org/wiki/Double-tuned_amplifier

Old radios with 11 MHz FM IF and 455 kHz AM IF used a dual ferrite slug double tuned IF BPF.

You might also call a critically-tuned filter of any order ,  with maximally flat response AND 0 dB ripple what kind of filter??___  Bonus question.