Bowing is one of the most visible products of martial arts training. It is also one of the most misunderstood concepts by not only beginning students but also those not familiar with the Asian culture. In the Asian mind set, the bow is not seen as a sign of subservience like it has been viewed in Middle East and Western cultures, but is rather a sign of respect and more mundanely as a simple method of greeting, much like a handshake is used in the "Western World" or even a military salute.
There are several forms of bowing, but they can be divided into three categories, formal, semi-formal and informal. An informal bow is executed by bending forward at the waist about 15 degrees. This informal bow is what is seen most often these days, however IT IS NOT or SHOULD NOT be used in martial arts training. Only the semi-formal and formal bows should be used.
The semi-formal bow is done by bowing almost 90 degrees at the waist with your eyes downward, with your hands at your side (do not slap your thighs) while standing at the position of attention. This is used the most and by keeping your eyes on your opponents feet, your able to tell if there is going to be an issue (attack etc) because they will need to move their feet to attack.
The formal bow is done in the kneeling position, with your knees together and your feet tucked under your hips. Your hands should be placed on your thighs and when you bend forward you will slide your hands to the floor forming a triangle and place your forehead within that triangle. Bowing represents the mutual respect that instructors and students should feel amoung themselves and towards each other. When you bow, you are not bowing to that person, but to the knowledge and skill that person has acquired, and to the rank that they have attained.