Bowing (Ojigi) is a very important custom in Japan. Japanese people bow all the time. Most commonly, they greet each other by bowing instead of handshaking. It is impolite not to return a bow to whoever bowed to you. Japanese people tend to become uncomfortable with any physical forms of contact. But, they became used to shaking hands with westerners.
Bowing has many functions in one. It expresses the feeling of respect, thanking, apologizing, greeting, and so on. It's a convenient and important custom for you to learn. You can bow, when you say, "Thank you", "Sorry", "Hello", "Good bye", "Congratulations", "Excuse me", "Good night", "Good Morning", and more!!
Bowing seems simple, but there are different ways of bowing. It depends on the social status or age of the person you bow to. If the person is higher status or older than you are, you should bow deeper and longer. It is polite to bow, bending from your waist. Men usually keep their hands in their sides, and women usually put their hands together on their thighs with their fingers touching. If it is a casual situation, you can bow like nodding. The most frequent bow is a bow of about 15 degrees. You might feel strange to do it, but try to bow in Japan. You will be considered very polite!