Brainwallets are like the mnemonic seeds generated by hardware wallets, however, the human user generates the words themselves and memorises them without any written record.
The mnemonic seed/ passphrase is never written down. It is 'stored' in the holder's brain.
If the holder forgets the passphrase (or becomes incapacitated), the money is likely lost forever - not a very secure storage method.
Creating randomness in passphrase words is extremely difficult to do by hand, therefore security is again compromised.
It is possible to use a [BIP 39] passphrase generator to get strong entropy/ randomness and optionally add a salt value for additional security, however storing anything in the human brain carries inherent risks.
Use a brainwallet at your own (high) risk.