General explanation for this and similar cases is very simple. The inhibition activity of a compound results from its efficient binding to its biological target, e.g. enzyme active site. In this bindinjg site, there is a specific spatial arrangement of functional groups participating in ligand binding. Then you should look at 3-dimensional structure of your lugand (not its planar representation drawn on a piece of paper). The configurations of R and S isomers of your molecule differ strongly – you can see that with a simple 3D molecular model. For example, in your particular case, if we keep CONH-containing ring in the horizontal plane, aminophenyl fragment in two enanthiomers will be below or above this plane. So there is a big 3D structural difference between isomers, they are just two very different molecules. One of them will be much more suitable for the interaction with a set of binding groups of target biomolecule with given spatial coordinates.

Another way to answer your question would be: because it interacts more strongly with this particular chiral receptor than the enantiomer does. You see, if the "environment" was achiral, the interactions would be identical (all the distances would be identical)... well, unless our chiral molecule itself induces asymmetric/anisotropic response, but that is still a different cup of tea.

Thank you very much Dubey and Jacek for your help.