Today, the Moon, second brightest object in the sky, has reached the First Quarter phase, which means that it is exactly 90 degrees around its orbit of Earth.
As for lunar mechanics, the Moon is always half lit. The reason we don't always see it as such is thanks to orientation in relation to us. Right now, with the Moon at a 90 degree angle relative to the Earth and Sun, we see the Moon as half lit and half dark, leading to the popular, erroneous phrase 'half Moon.'
After today, we will see more and more of the Moon as its lit side turns more toward us as it heads for a straight line in Sun, Earth, Moon order, and thus Full phase.