Holy ground acts as a sanctuary for immortals. According to their rules no immortal combat may occur on Holy Ground. Whether this means that immortals may not fight or may not kill on holy ground is debatable.
There is some indication that an immortal may kill a disabled or passive immortal on holy ground with no negative repercussions though this is almost entirely speculative (see the Sanctuary). There is a legend / rumor that prior to the eruption of Vesuviius two immortals were battling in a temple of Apollo. Generally only the most evil or deranged immortal would attempt to engage in combat on holy ground.
What exactly qualifies as holy ground and how an immortal can know the ground is blessed is never explicitly stated. There are cases of qualifying holy ground including land blessed by non-Christian faiths and clergy but there is no explicit statement as to how two immortals would know of a patch of ground's status unless it were indicated to be holy via markings etc. It is possible that should the immortals engage in combat there would be immediate indications that the rule was being violated such as earth tremors etc. such as during the fight between Connor MacLeod and the warrior Kane in 1994.
That said, in Kurgan Rising Duncan is lured into taking another immortal's head on consecrated ground. Macleod notes that he should have instinctively realized the ground was consecrated implying that the immortals have an ability similar to their Buzz that acts as a warning system. It is later revealed that the building Duncan committed the transgression in had been specifically designed to channel such an act and allow the mad mortal who built it to resurrect the Kurgan implying that something about the structure itself crippled MacLeod's warning system.