The idea behind "admits a classification in the sense of Shelah" is that the class of models of $T$ in a given cardinal $\aleph_\alpha$ can be described by bounded many numercial invariance (generalizing the situation that a vector space is determined by its dimension). In the case of a countable first-order theory $T$, if $T$ admits classification then the number of isomorphism types of models of card $\aleph_\alpha$ is bounded by $\beth_{\omega_1}(|\alpha|)$. When $\alpha$ is such that $\aleph_\alpha$ is much bigger than $\alpha$ then $\beth_{\omega_1}(|\alpha|)<< 2^{\aleph_\alpha}$.
Thus $I(\lambda,T)=2^\lambda$ for all uncountable lambda implies that $T$ is not classifiable.
