When we calculate logP, the configuration of atoms in the molecule can be such that it can trigger a secondary effect on the distribution of the molecule in the octanol/water system. This is typically an intra-molecular effect such as H-bonds or effects of ionized groups onto each other etc. This is expressed in the structural increment, which is then added to the regular sum of atomic logP contributions. This increment is usually fine-tuned in our model to express the secondary effects of intra-molecular forces.
We have a short description of our logP model with references as well here: