Why is my MacBook Air asking for Password as I have only set-up Finger Print to unlock it?

You need to provide a password the rebooting the Mac. You will also need to provide the password about once a week even if you do not restart your Mac. Plus the password is required for some functions instead of the TouchID.

See this Apple article for more details:

About Touch ID advanced security technology - Apple Support

siddhi_tandon wrote:

I remember I only applied my fingerprint while doing my laptop setup

follow steps here https://support.apple.com/en-us/HT202860

in order to use touch id, you would need to set up a 4 to 6 digit passcode.