Anatase TiO2 attracts considerable interest for a range of technological applications such as photocatalysis and electronic memory devices. Recent studies have shown that the (001) surface plays a crucial role in its photocatalytic activity and this has been attributed to its higher surface energy and its ability to adsorb water dissociatively. However, a fundamental understanding of why this surface is so unique is still lacking. In this study, the anatase TiO2 (001) and (101) surfaces, both present in its equilibrium crystal shape, are studied using state-of-the-art ab initio hybrid density-functional-theory calculations. It is found that the electronic states at the (001) surface strongly deviate from the bulk, while the electronic states at the (101) surface do not. We illustrate the role of anisotropy in the crystal on the electronic structures of anatase TiO2 and demonstrate how the formation of the (001) surface disrupts local orbital interactions and gives rise to distinctive surface electronic states, which give the (001) surface its unique properties.