The Dhammapada  5 & 6

“Hatred is indeed never appeased by hatred here. 
It is appeased by non-hatred - this law is eternal.”

This pair of verses (DhP 5 and 6) is very close in meaning to the previous pair (DhP 3 and 4). Again, a very simple truth, that most of the religions in the history have stressed again and again. The only cure for hatred is the abstention from it. Never can we stop people from hating us by hating them. In this way, mutual hatred will rise -- often to the point when hatred gives way to violence.

The only way to stop this chain of hatred is to stop hating, of course. As the verse says, this is an eternal law. It was always so and always will be. One can only wish that we could remember this verse in all situations and deal accordingly. How many wars, how much suffering could be easily averted just by taking the advice of this short verse seriously.

“The others do not understand that we should restrain ourselves here. 
Those who understand that, therefore appease their quarrels.”

This verse is related to the previous one (DhP 5), even if this relation is not apparent immediately. In DhP 5 we are told that hatred can not be appeased by hatred but only by abstention from hatred. Here it says that some people do not understand this, do not know that we should restrain ourselves, that we should not give in to hatred. Those who realize that, of course, stop their enmity and quarreling, thus stopping hatred completely.

By the word "others" the authors probably meant the people, who do not realize this eternal law (that hatred can be appeased by non-hatred only). The use of the word "here" ("that we should restrain ourselves here") suggests this world, our present situation. It can also point to the previous verse -- then we should understand "here" as "this" (meaning this eternal law of appeasing hatred by non-hatred).