The water snakes represent the beauty and blessedness of God's creation. The Ancient Mariner calls them "happy living things" as he watches them swim in the sea, their colors flashing with a "golden fire." They also represent the Mariner's moment of redemption.
The Mariner has been cursed for his killing of the albatross. It this point, he has been suffering intensely on board a ship that is marooned in the middle of a perfectly still sea that is so dead and unmoving that it looks "painted." The rest of the crew has died, and the Mariner has been haunted for seven days by the look in their dead eyes. He is parched with thirst. In the midst of all this, the Mariner sees the water snakes and is able to appreciate their beauty and feel a "spring of love" for them which "gushe[s]" from his heart. He blesses them. The love and connectedness he feels towards the water snakes releases him from the curse. The albatross falls from around his neck. It rains, the dead crew rise and return to their posts, and the ship moves again.
When he sees the water snakes, the Mariner is transformed because now he can see, love, and bless the creatures of nature as worthy parts of God's creation. Previously, when the Mariner kills the albatross, he is unable to see the bird as a precious creature. Once he can perceive that that water snakes are "living things," worthy of love and blessing, he can move forward, reintegrated into God's kingdom.