葛 is kudzu, a vigorous climbing vine native to East Asia (the same plant infamous as an invasive species in the American South). Because the vines twine around each other in messy snarls,
葛藤 became a stock metaphor for complicated human entanglements — disputes, debts, romantic complications. In Chan/Zen Buddhism,
葛藤 even refers to the verbal tangles of doctrinal argument.