A password manager is a software application that stores passwords, passphrases, credit card numbers, PINs, TANs, security questions, PGP encryption keys, and other valuable information securely and allows for easy and fast access by the user.
The information stored within a password manager usually is encrypted using a single strong master password. This password has to be provided to gain access to its information. A password manager allows you to use different strong passwords for every website you log in to, every system you use and every application that requests password authentication. All without having to worry about remembering more than one master password.
Most password managers additionally offer a password generator letting you generate strong passwords using alphanumeric, special and punctuation characters in random order.
Many password managers even integrate seamlessly into your device. They allow you to easily filling password fields of websites, or letting you copy/paste passwords into other applications.
Thus, password managers simplify your entire user experience when dealing with secure password authentication.