This message is significant because it represents the ultimate sacrifice Harry Potter makes. He chooses to die in order to break the curse on the Horcruxes, effectively "closing" the cycle of death and violence.
It's important to note that the Snitch itself isn't a Horcrux. It's a personal object of Voldemort's that he used to transport the message. The true meaning of the message is revealed when Harry opens the Snitch to find the scroll. This action, combined with Harry's choice to die, is what allows him to "close" the cycle of death and violence and ultimately defeat Voldemort.