The results are reported of ab initio calculations on the magnetic ordering in NiO, a prototype of the antiferromagnetic insulator. By analyzing wave functions for different cluster models, information is obtained about the physical effects determining the sign and the magnitude of the magnetic coupling parameter J. The role of the edge oxygens, surrounding the essential unit (Ni2O), is found to be quantitatively important but purely environmental in contrast to the role of the bridging oxygen. Furthermore, the importance of electron correlation and the usefulness of pseudopotentials in the calculations is investigated. The final result for J compares reasonably with experiment (about 50%), and possible sources for the remaining discrepancies are discussed.