Why a password maanger? Password managers help you store and remember passwords for all the different sites you access both at school and at home. It is highly advisable to use different passwords for every site you visit yet without a password manager, it's nearly impossible to keep track of them all.
LastPass: This is an extension usable in chrome and firefox browsers that will use a master password that unlocks access to all your saved passwords. It accomplishes this by way of a single password that you will need to remember. Your passwords are stored on the cloud but they are encrypted and even LastPass has no access to them.
Pros: You can install the browser extension on any phone, laptop or other device, login and have access to your passwords anywhere. Works on Mac, PC and Linux as well as common phones such as android and iPhone and most tablets.
Cons: Your passwords are stored on LastPass' servers so should something happen to that company, you might lose access to them. It might be a good idea to back them up from time to time. Also, LastPass is not open source so the source code is not able to be inspected to see if it really does what the authors say it does.
Keepass: This is a full downloadable app that encrypts and stores your passwords locally on your own computer or on a portable drive such as a flash drive. As with LastPass, you use a single password to unlock the encrypted passwords it saves.
Pros: Open source. The code is available to prove that it does what it says. It works on windows and on linux through an emulator. There are separate programmers who have developed it from the source code for phones and macs and other platforms.
Cons: Does not work for mac or native linux unless you get one of the ported project copies (see Pros). These ports are not official but work. You have to carry a copy of your passwords with you (or store the full database on a portable drive that you take with you) to use it away from your desk/home.