It means "many times" but sounds more poetics. Here's one example from a book: "Many are the times that I have left the hunting fields at the end of the day and looked into the twilight to see the silhouette of hunters and dogs heading home, all of them my friends." It means: "I have left the hunting fields at the end of the day many times and looked..."

It means there are many times a particular event, thought or action has occurred. "Many are the times I yearn to be free." It is similar to "many a time".