Ano Hana's opening mentions "misanga". What exactly is that?
A misanga is a type of handicraft good luck charm, similar in concept to friendship bracelets, they are typically made from knotted embroidery floss, thread, gimp, or similar material. Like friendship bracelets, they are tied together by simple knots. 

It is said that if you make a wish when you tie the ends together, your wish will come true when the bracelet falls off from wear. 

The etymology of the name seems to come from the Portuguese word for "beads" (miçanga). They were first popularized in 1993 during the beginning of the J-League, the Japan Professional Football League. Ramos Ruy and Tsuyoshi Kitazawa of the Tokyo Verde football club wore these to wish for the victory of their team. 

The idea behind it may have changed but it's intended to be a symbol of good luck and friendship.