What does it mean?
The famous side-to-side head wobble is Context Dependent. It usually means "I
understand", "Okay", or "Acknowledgment". It rarely means "No".
Fast Wobble: "Yes, I understand."
Slow, Soft Wobble: "Maybe" or "I am listening."
It's Not a "No"
In the West, shaking the head side-to-side means "No". In India, the wobble (tilting ear to shoulder) is a sign of engagement. If you ask a taxi driver, "Do you know the way?" and he wobbles, he means "Yes, get in."
Why Do Indians Do It?
It is a polite way of being respectful. Direct eye contact with a rigid posture can sometimes be seen as aggressive. The wobble softens the interaction.