Q: why my macbook air (2014 os mavericks) backlit is not work automatically when in the dark environment?

Hi ..

Try here >  Portables: Adjusting the keyboard backlight

If nothing there helps, reset the SMC >  Intel-based Macs: Resetting the System Management Controller (SMC)

If that doesn't help, take the Mac in for service. It's covered by the one year limited warranty.

If this is a new MB Air, you have 14 calendar days from the date you received the Mac to initiate a return as noted here.