It’s like a “sign that reveals something hidden”. It’s often said as “telltale signs”. For example, you might say “these are the telltale signs of alcoholism” if you went to someone’s house and there was a half empty bottle of whiskey on the counter at 9 in the morning.

A telltale comes from sailing. They're little bits of yarn attached to the sail. They let you see what the wind is doing. The wind being invisible, a telltale shows you what you can't normally see. In nonsailing use, a telltale is a small thing that shows you the whole truth.