The word zigzag describes the shape of a line. A line drawn in a zigzag shape makes a lot of short, sharp turns. The letter Z is a zigzag itself, and a thunderbolt is also often represented as a zigzag.
The first turn a zigzag line makes is called a zig, and the second is called the zag. Zigzag can also be a verb. If you're describing how you got lost in the desert, you might say, "I meant to go straight, but then I zigged, and then I zagged." Serpentine describes a line that curves, but the curves are rounded (like a serpent), not short and sharp like a zigzag.