This is the Girls Guild Secret Handshake.

To make it, hook the first four fingers of your right hand into the first four fingers of the right hand of the person shaking hands with you.  Then each thumb goes around the back of the other person’s fingers.

As you can see, the two hands form two interlocking letter G’s, each starting at the tip of the thumb as the top of the G and curling around the pointer finger for the rest.  The letter G’s stand for Girls Guild, but they also stand for the Girls Guild motto:  Be Gentle and Good.