The ELI5 explanation:

Your password simply encrypts your seed within your wallet file. If you have your wallet file, then you can use your password to decrypt your wallet file to get your seed (and access to your funds). If you have your seed, then you can simply create a new wallet file with your seed to get your BTC.

If you recently formatted your HDD, then you may be able to recover your wallet file with file recovery software. If you had any significant amount of BTC in your wallet then you should stop using your computer that your wallet was stored on immediately (do not even touch it), and use a second computer to download file recovery software to search your formatted HDD for your wallet file.

If the file recovery software cannot find a good version of your wallet file, then you may wish to bring your HDD in to a computer repair shop who may be able to recover your wallet.

If you have any backups of your wallet, then you can skip all of the above, and use the backups.