To teeter is to waver or sway a bit from lack of balance. When people first learn to ride a bicycle, they inevitably teeter for a while before becoming more skilled and confident.
A beginning gymnast will teeter on the balance beam, and anyone who's not accustomed to high-heeled shoes will teeter as they walk in them. Figuratively, you might even teeter, or hesitate, between two hard choices. A "teeter-totter," or seesaw, is a playground toy for two people, a long board fixed on a center support, designed so that when one kid is down, the other is up.