I am confused and I have the following questions:
1. What are (in the context of article below) protein cavity centres?
2. How are they related to binding?
As you can find under the table with cavity centers in pdf version of this article:
The table lists the protein’s PDB ID, the ligand considered and the specified cavity center. 22 ligands are similar to hexoses in shape and/or size. The cavity center is the centroid of the reported PDB atom numbers.
And a little later:
The binding-site center is computed as the hexose pyranose ring centroid for the positive examples, and as the ligand or empty pocket centroid for the negative ones. The hexose pyranose-ring atoms are located up to 2.9 ̊ A away from the ring’s centroid. Since some atomic interactions can be important up to 7 ̊ A , we consider the binding-site as all protein atoms present within a 10 ̊ A radius sphere around the binding center. All other atoms are discarded.
So basically @aandreev is right. You can read about centroids here