Anjali mudra is not merely a way to greet someone with respect. Anjali mudra is a gesture that serves two key purposes.
The first aspect reflects knowledge of the self and supreme: that the same God who is within you keeping you alive is also outside the self to support your existence. The same is true with every being in the world. This knowledge makes one obedient to fellow beings, fellow creatures, and the environment. And thus, one’s head automatically bows down in humility. The gesture thereby creates a sense of positivity, calmness, and respect toward the recipient and inward with the doer.
The second aspect is that the gesture reflects submissiveness in the doer to seek God’s protection.