Electronic signature serves to verify the ownership of the bitcoin address. If the user sends a valid electronic signature, it is verified then that he/she is the owner of the bitcoin address and that the bitcoins are being send from this address by him/her.
Electronic signature may be acquired if you let the message containing your e-mail address (stated during registration) signed. Insert the acquired sequence of characters in the field "Electronic signature" (in the menu "My addresses" in your profile after clicking the button "Add new address").
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Wallet Trezor manual