Both objects display a crescent phase for the same reason – a combination of the relative positions of the Earth, Sun, and Venus. However the Moon orbits the Earth while Venus orbits the Sun meaning that as each day passes the Moon moves further eastward away from the Sun, increasing the angle between the Earth and the Sun allowing the Moon to increase, wax, toward full Moon. At the same time Venus is moving westward toward the sun, decreasing the angle and causing Venus to not only decrease, wane, in phase appearance, but also increase in size as it moves closer to the Earth.
If the latter is confusing picture Venus orbiting around the Sun and soon coming between the Earth and the Sun. From a perspective above the solar system planets orbit counterclockwise. As this graphic shows Venus is almost in line with the Earth and Sun. When they are aligned on 11 January Venus will be at what is called inferior conjunction. And as Venus continues to orbit the Sun it will gradually move away from the Sun , increasing the angle and increasing, waxing, in phase appearance. Interestingly as Venus does this its apparent size will decrease because Venus will then be moving away from the Earth.
Some previous posts about a crescent Moon and Venus:
Daytime Venus Sightings – 5 December 2013
Crescent Moon and Venus – 5 August 2013
Click here to go to the Qué tal in the Current Skies web site for more observing information for this month.