To put on air and graces (BrE) or put on air (AmE)-
Somebody "put on airs and graces" o "puts on airs", when they behave in a
way that suggests that they want people to think that they are more important
or sophisticated that they really are: Bella put on air and graces, remaining a real Blackpool girl.
Source: Larousse Guide to Idioms- Chambers Publishers.

Verb 1. put on airs"
put on airs - act like the master of; "He is lording it over the students act superior, lord it over, queen it over
act, move - perform an action, or work out or perform (an action); "think before you act"; "We must move quickly"; "The governor should act on the new energy bill"; "The nanny acted quickly by grabbing the toddler and covering him with a wet towel"
Source:         http://www.thefreedictionary.com/put+on+airs

http://wiki.answers.com/Q/What_does_put_on_airs_mean?
If someone is "putting on airs" it means that he or she is acting superior or snobbish.

put on airs
v.
brag, show off, make pretensions; see strut.

http://www.yourdictionary.com/synonyms/put-on-airs

put on airs idiom
Assume a haughty manner, pretend to be better than one is, as in I'm sick of Claire and the way she puts on airs. Airs here means “a manner of superiority.” [c. 1700]
http://www.yourdictionary.com/idioms/put-on-airs