Those random words are the master seed. Usually you don't enter the master seed to use your wallet. Your wallet encrypts the master seed and unlocks it with a password of your choosing. I suppose they are talking about the password to the wallet, not the Bitcoin keys.
No you don't have to remember the master seed. You should write it down and hide it somewhere, though. You need it if you lose access to your wallet. (It's a bit like a backup of the encryption keys for your hard disk, if you have enabled disk encryption).
The wallet password depends on the wallet of course. I guess you often create it yourself or it may even be optional.
I wouldn't recommend that approach for storing large amounts.
