If something moves in a serpiginously way, it moves like a snake, in a winding and twisting path.
The word serpiginously makes people think of snakes and twisting paths.
Examples:
The river flowed serpiginously through the forest.
The road wound serpiginously up the mountain.
The vines grew serpiginously around the tree.
The hose twisted serpiginously as the water sprayed out.
The roller coaster track twisted serpiginously through the amusement park.
The path to the treasure led serpiginously through the dark cave.