Secure long-term backup and storage of secrets is of particular importance to Bitcoin users. So far various techniques have been used including storing plain text private keys and password encrypted private keys on paper.
Storing plaintext private keys has the obvious drawback that anyone who sees it can steal your funds.
Storing password encrypted private keys has another drawback. You turn your private key into two components, where both are needed to reveal the private key. While you prevent someone getting one component from revealing the private key, you make it more likely that you lose control over your private key yourself. If you lose one component due to flood, theft, or fire, you will have lost control over your private key.
With this secret sharing scheme, if you discard one of the shares right away (making it a 2-of-2), you have a setting comparable with classic password encrypted private keys, with the added benefit that both components are equally strong. The availability of the third share simply provides additional flexibility.