When did I buy my MacbookAir?

Look at your purchase invoice / receipt.

Or enter your serial number here: Check Your Service and Support Coverage - Apple Support

Your purchase date would be one year before the Expiration date of your Warranty / Support coverage.

If its already expired, if will not show a date, so you know its been more than a year since the device was purchased from Apple or an Authorized reseller.

If you need the actual purchase date, and you bought from Apple within the past 18 months, it's listed here:

https://secure2.store.apple.com/shop/order/list?hist=545

Else, you would need to have kept such records yourself (perhaps search your email, if you bought online).

If what really need to know is the age of your Mac, you can find the model year in Apple menu > About this Mac.