This is the 11224th most frequent Russian word.
давние
"Long-standing" or "ancient."
Here, "давние" modifies the word "знакомства" (acquaintances), indicating that the acquaintanceship has lasted for a long period.
У нас с ним давние знакомства.
He and I have longtime acquaintances.
In this sentence, "давние" is used to describe "деревья" (trees), suggesting that the trees have been there for a considerable amount of time.
Давние деревья окружали старый дом.
Ancient trees surrounded the old house.
"Давние" describes "традиции" (traditions), expressing the idea that the traditions are significantly old and respected because of their age.