Q:

What is a finger tied with a knot or bow called?

What does this image represent?

I understand from context that it supposed to mean "remember" but I don't see why this icon is used for that. 
Is there an idiom or saying that is connected to this image?

A:

It is used as a reminder:

a person or thing that makes you remember a particular person, event, or situation.

The notion of a knot used as a reminder probably originates from the custom of tying a knot in the handkerchief: 

In days gone by, gentlemen would tie a knot in their handkerchief to remind themselves there is something that should not be forgotten. Whenever they reached for their handkerchief, they would be reminded. I believe that tradition is connected with the Greek myth of Ariadne. She was the daughter of Minos and Pasiphaë who gave Theseus the thread with which he found his way out of the Minotaur’s labyrinth. I love taking photos of the threads and knots I find in the streets. Even if these knots were not made consciously by people to remember something, they might as well have been. It triggers my imagination and adds the sense of confusing navigation to the labyrinth of the city.

