What does this "place" mean?

to try to "place" someone means to try to remember where you know them from. You would never try to place someone who was a total stranger to you, because trying to place someone only happens when they seem familiar to you, but you cannot remember why they seem familiar to you.

Thank you a lot, Eos.

To identify or classify in a particular context, for example:

could not place that person's face.

(From AHD)