When you manage your own Monero Account with the private @spend-key, you are solely responsible for the security of your funds. Thankfully, Monero makes it very easy to backup your account. When creating a Monero account for the first time you will be given a unique @mnemonic-seed for your account that consists of 13 or 25 words in the language of your choosing. **This seed is the only thing you need to backup for your account**, and so it is imperative that it is written down and stored securely.Never store this seed in a form or location that would allow someone else to see it!
The private keys for both of these must be protected by you in order to retain your account privacy. On the other hand, the public keys are obviously public (they are part of your Monero account address). For normal public/private key cryptography someone could send you a private message by encrypting it with either of your public keys, and you would then be the only one able to decrypt it with your private keys.
winslow