HIN stands for Holder Identification Number. It is a unique identifier and is similar in concept to a bank account number.
If you have a broker, the broker uses this HIN when buying or selling shares for you. The HIN ensures that when buying shares they are registered in the correct name, and when selling shares that the correct shares are being sold.
This process is what is known as broker sponsored. This means that the shares are held in your name with that broker.
If you use more than one broker, each broker will have created a different HIN for you.
When you buy new shares through OnMarket, if you provide your HIN when setting up your investment profile, the shares will be registered in your name and will appear in the brokers account associated with your HIN.