The Great Serpent is a creature that totally changes the dynamic in Sekiro: Shadows Die Twice. Where every other huge monster you encounter can be battled, parried, and defeated with your sword, the huge white snake is a literal god, and you can't just face it down and destroy it. When you first encounter the snake, your only way of dealing with it is through cunning and stealth--as seen in the video above.
The serpent shows up for the first time as you're venturing through Ashina Outskirts on your way to the castle. You'll want to return sometime later to the Underbridge Valley area where you deal with the snake, because there's a key item to be found here: Snapseeds. These handy items give you an advantage in certain fights with enemies who use apparitions against you, most notably Lady Butterfly.
This isn't the last time you'll run into the Great Serpent in Sekiro, but we won't spoil that for you just yet. But we've got plenty of other Sekiro guides if you're looking, including ones on where to find some key early-game prosthetics, and how to beat the Chained Ogre, the Blazing Bull, and Juzou the Drunkard.