Pulling air into the mouth can awaken and activate the taste buds. Air flowing over taste buds acts like liquids or solids coming into contact with them. Therefore, pulling air into the mouth after drinking something can help a person use their taste buds to sample the odor of the substance.
I think its because some extra air aids in getting the pressures right for swallowing. The drinker could just open her mouth, but then the liquid could fall out. The pursed-lips thing ensures that air comes in but no liquid comes out.
Males may be trying to take in more air so they can belch afterwards. This impresses other men. Women may do it just to look cute and sexy, or to get more of the beverage off of their teeth. It is possible that both genders think it looks attractive to others.