and measures how much our estimator fluctuates due to finite-sample effects. Combining these expressions, we see that the expected out-of-sample error of our model can be decomposed as $$ E_\mathrm{out}=E_\mathcal{L, \epsilon}[\mathcal{C}( \boldsymbol{X}, \hat{g}(\boldsymbol{x})) ] = Bias^2 + Var + Noise. $$
The bias-variance tradeoff summarizes the fundamental tension in machine learning, particularly supervised learning, between the complexity of a model and the amount of training data needed to train it. Since data is often limited, in practice it is often useful to use a less-complex model with higher bias – a model whose asymptotic performance is worse than another model – because it is easier to train and less sensitive to sampling noise arising from having a finite-sized training dataset (smaller variance).