The BoxCryptor Drive with the plaintext files is purely virtual and does not really exist. Only the encrypted files do physically exist on your hard disk. As soon as you exit BoxCryptor, the BoxCryptor Drive is removed and no plaintext files are available anymore.
BoxCryptor asks for the password when the BoxCryptor Drive before the BoxCryptor Drive gets created. Without the correct password, it is impossible to decrypt any file and the BoxCryptor Drive won't be created. When the BoxCryptor Drive has been created, BoxCryptor will not ask for the password again, until the BoxCryptor Drive has been removed again.
By default, BoxCryptor suggests to remember the password. This means, that the password is stored (in encrypted form and only available to your Windows user account) on your local hard disk and used for creating the BoxCryptor Drive in the future so that you don't have to enter it.
This is optional and can be changed. When entering the password, simply uncheck the "Remember this password" and you will always have to enter the password first. If the password is already remembered, you can clear it by clicking "Clear Stored Password" in the BoxCryptor Preferences' toolbar.
Please note, that the main purpose of BoxCryptor is to secure your data in the cloud, e.g. when stored at Dropbox or Google Drive. In order to secure your local computer, please refer to other security options and/or specialized software if you have further requirements. E.g. use passwords for power-on or the hard disk in the BIOS of your computer.