Warring means fighting a war against each other. It is an adjective, and it almost always sits in front of a noun — you say "warring countries" or "the warring sides", but you do not usually say "the two countries are warring" (for that, people say "are at war" or "are fighting"). The nouns it goes with are nearly always groups of people, not single people: warring nations, warring tribes, warring factions, warring families, warring gangs. That is a small set of partners, so if you learn the phrases you have learned the word.

The word carries a feeling that the fighting has been going on for a long time and neither side is winning. A news writer picks "warring" when they want you to hear "this mess is old". Because of that, it is common in writing about history, politics, and news, and rarer in everyday talk.

It also stretches away from real war. "Warring emotions" or "warring desires" means feelings inside one person that pull against each other — you want to go and you want to stay. "Warring theories" means ideas from scholars that cannot both be right. Nobody is shooting anyone; the point is only that two things cannot live together peacefully. This stretched use is common in books and essays.

There is also a verb "to war", but it is old-sounding and rare now. Most people meet "warring" only as the adjective.