You may find this video helpful for gaining a conceptual understanding.
The Most Misunderstood Concept in Physics
Historically, there have been a few statements that all independently converge on the second law of thermodynamics, which are as follows.
Clausius
No system can operate such that the sole result is heat transfer from a cold body to a hot body.
Kelvin-Planck
It is impossible for a cycle to produce work while receiving energy from a single thermal reservoir.
Entropy Statement
It is impossible for a system to destroy entropy
Now, the third articulation is admittedly not particularly useful until we define entropy, but we will get to that later.
For now, we will consider the first two articulations, and how they put bounds on our coefficients of performance. Recall the system which we analyzed for power, heat, and refrigeration cycles.
$$ W_{sys}=Q_H-Q_C $$
We may observe that the Kelvin-Planck articulation puts a limit on our coefficient of performance for a power cycle. For multiple thermal reservoirs to be at play, some of the heat transfer from the hot reservoir must go towards the cold reservoir, rather than all to work. As such, the work will be less than the heat transfer, and the coefficient of performance less than one.
$$ Q_C>0\Rarr W<Q_H\Rarr\eta<1 $$
Additionally, we may observe that the Clausius statement puts a limit on the coefficient of performance for refrigeration and heat pump cycles. For a heat pump and refrigeration cycles, $Q_H,Q_C$ both happen in the reverse of the direction illustrated. In order to satisfy the Clausius statement, $W$ must occur in the reverse of the direction illustrated as well. As such, theses coefficients of performance cannot go to infinity.
$$ Q_H<0,~Q_C<0\Rarr W<0\Rarr\gamma<\infin,~\beta<\infin $$
We may make a few final statements about the coefficients of performance, $\eta,\gamma,\beta$ for cycles using thermal reservoirs of the same temperature. For one, the coefficient of performance of a reversible cycle will always exceed that of an irreversible cycle. Additionally, the coefficients of performance of two reversible cycles will always be identical.
These boundaries exist because real world processes contain irreversibilities which produce entropy, deviating from the ideal performance of reversible processes. Examples of irreversibilities include heat transfer through finite temperature differences, unrestrained gas expansion, spontaneous chemical reaction, spontaneous mixing, friction, current through resistance, magnetization or polarization with hysteresis, and inelastic deformation.