A 13 or 25 word phrase used to backup a Monero account, available in a number of languages. This 25-word phrase (13 words in the case of MyMonero) has all the information needed to view and spend funds from a Monero account.
In the official wallet, the mnemonic seed comprises 25 words with the last word being used as a checksum. Those words correspond to a 256-bit integer, which is the account's private spend key. The private view key is derived by hashing the private spend key with Keccak-256, producing a second 256-bit integer. The corresponding public keys are then derived from the private keys.
By storing the 25 word mnemonic key in a secure location, you have a backup of your private keys and hence all of your Moneroj. Sharing this 25 word key is the equivalent of allowing another person complete access to your funds.
It's not a good idea to store more than you want to lose in a "hot wallet" aka a wallet which is currently or has ever been connected to the internet or loaded onto any device that has or may in the future be connected to the internet or any untrusted source!
By creating a cold, or paper wallet you can safely store Moneroj.