The origins of this tentacled tradition began in 1952 when fewer NHL teams meant that the road to the Stanley Cup only took eight playoff wins. Thus, the 8 legs on an octopus would symbolize the road to the Stanley cup with 8 winning games. Since then, hundreds of octopi have rained down onto the Redwing rink.
A list of recommendations state that the octopus should be cooked, as a raw octopus tends to leave slime on the ice. Link