A bow is a physical display of respect.
In Japan, there are different bows for different situations. This can vary depending on the relationship between those who are bowing: a first meeting between them, the occasion, etc. A typical bow lasts a second or two, but depending on the importance of the person bowed to, it can last longer. The more important the person is, the longer the bow should be.
To execute a bow, keep your feet together, and simply bend your upper body forward at the hip (at about a 45 degree angle), keeping your torso straight and your hands at your sides. Bend your elbows in relation to your body. Hold for a second or two, then stand straight.