While Bitcoin addresses appear to be a string of random numbers, they are actually computed from a private key. Private keys are long strings of random characters generated by your Bitcoin wallet software. There can only be one address generated from your private key, thus your private key is both the seed and password to your Bitcoin address.
The private keys are normally hidden by your Bitcoin wallet, but they can be occasionally printed on paper as a physical backup. They should never be shared publicly as they control access to your funds.
Bitcoin private keys generally contain 51 characters and start with a 5, such as in the following example: