The moon is pictured in the first quarter phase. When the moon is in the first quarter the right side of the moon is lit up. This phase is between the waxing crescent and waxing gibbous phase. The first quarter moon rises at noon and sets around midnight the next day. The moon is overhead at noon. The reason that it's not called the first half is because the moon is only one quarter of its way around the orbit of the earth. The first quarter moon comes about a week after the new moon from the previous week. The best way to describe this is that the moon is 90 degrees angle with respect to the earth and sun. The moon goes through a complete phase cycle in about a month, The lunation cycle takes approximately 29 days to complete. 

http://earthsky.org/moon-phases/first-quarter