Typical brain development follows a protracted trajectory throughout childhood and adolescence. Deviations from typical growth trajectories have been implicated in neurodevelopmental and psychiatric disorders. Recently, the use of machine learning algorithms to model age as a function of structural or functional brain properties has been used to examine advanced or delayed brain maturation in healthy and clinical populations. Termed 'brain age', this approach often relies on complex, nonlinear models that can be difficult to interpret. In this study, we use model explanation methods to examine the cortical features that contribute to brain age modelling on an individual basis. In a large cohort of n=768 typically-developing children (aged 3-21 years), we build models of brain development using three different machine learning approaches. We employ SHAP, a model-agnostic technique to estimate sample-specific feature importance, to identify regional cortical metrics that explain errors in brain age prediction. We find that, on average, brain age prediction and the cortical features that explain model predictions are consistent across model types and reflect previously reported patterns of regional brain development. However, while several regions are found to contribute to brain age prediction, we find little spatial correspondence between individual estimates of feature importance, even when matched for age, sex and brain age prediction error. We also find no association between brain age error and cognitive performance in this typically-developing sample. Overall, this study shows that, while brain age estimates based on cortical development are relatively robust and consistent across model types and preprocessing strategies, significant between-subject variation exists in the features that explain erroneous brain age predictions on an individual level.