记 here literally means record, you can often see it in story names, XX记 = story of XX.
such as 西游记, and the original name of 红楼梦 is 石头记, story of a stone.
Translating is not always word-for-word, I guess 老友记 may be more attractive than 朋友们 as a TV Drama name. BTW Friends has several different translations, another one is 六人行