This is just a game of watermelon splitting (スイカ割り). In anime and manga, it is common activity portrayed in the beach chapters. Generally, the game is also played at the beach in real life, but it may also be played in nursery/kindergarten/playground or at event venue.
The rules of the game is quite similar to piñata: the watermelon is laid out, and the participants will try to smash it open while blindfolded.
The 2 paragraph above are summarized from Wikipedia page, both English and Japanese version.
There is no significant symbolization here. It is just a game in Japan introduced by Saito to the denizen of Halkeginia. By using the reason "for the sake of the Spirits of Water", the principal (+ Saito) fools the girls to change into bikini from one-piece swimsuit. And since the game is played blindfolded, the boys can ogle at the girls body all they want without triggering the girls self-consciousness.