We define information gain as $IG(X,Y) = H(Y) - H(Y\mid X)$.

We interpret information gain as the amount of information we learn about the label $Y$, given a specific feature $X$.

Note that if the feature $X$ is completely uncorrelated with the label $Y$, then $H(Y\mid X) = H(Y)$. Therefore $IG(X,Y) = 0$.

As such when we choose the next feature to split on we should choose the one that maximizes information gained.