A password manager isn't going to protect you from government 'dragnet' surveillance, but it is an increasingly important part of staying secure online, especially when paired with two-factor authentication.
Most password managers work the same way: you will setup an account with a (preferably strong) master password and it will then store credentials for the sites you tend to visit, either manually or through an automated function in the app.
So what makes a good password manager? A strong commitment to security, easy user experience, functionality and price are all factors here. Here are the best password managers.