This question comes up a lot in my field of work, and unfortunately, there is no rigorous answer. Everybody seems to have a different (albeit loosely similar) definition of a margin of conservatism. However, we all need a definition, as it drives much of the model development and validation work at financial institutions. Furthermore, AIRB risk parameter estimation models require a margin of conservatism, which are thoroughly assessed by our regulatory agencies (e.g. OSFI in Canada).
For me, a margin of conservatism is broadly defined as the additional amount in model estimates relative to actual outcomes. This definition will differ depending on the model in question; where for some it may be interpreted as low threshold above some metric of accuracy, while others may require a much higher threshold. Certainly, conservatism may be considered as a back-testing objective, whose definition may be moulded to the purpose of the model being tested.
For example, when calculating LGD for economic capital, estimates might be low enough to be an accurate representation of the portfolio, yet on the side of conservatism to ensure underestimation is kept to a minimum . However, stressed LGD estimates should be inherently inflated to provide a cushion during economic downturn periods.
There are a few ways in which margins of conservatism can be embedded into model estimates (and when I say "estimates", I generally refer to risk parameter estimates): implicitly and explicitly. Implicitly refers to embedding a 'cushion' in the model by modifying data, regression coefficients, running a quantile regression, etcetera, in order to push upward the final model outputs. Explicitly refers to taking unmodified model outputs, and pushing these upward by quantifying a separate additive/multiplicative scaling factor or procedure. Plainly running a regression (that minimizes some measure between actuals and predictions) on historical data will produce you predictions that are roughly similar to your actuals. This is not conservatism, this is accuracy, and there is a trade-off between these two states. Juxtaposing how much one is favoured over the other, and quantifying this distance, is subject to opinion.
In summary, institutions incorporate margins of conservatism in their risk parameter estimates to capture certain modelling deficiencies, uncertainties, risks, or to simply abide by the regulatory framework imposed on them. The quantification of such ranges vastly among institutions and models, and seemingly, there is no universal way to quantify this "margin".