When you visit a site you've got an account on, the browser extension notices and can populate your user/pass into the login fields, and optionally automatically log in. It can also generate random passwords of any length and complexity, and automatically create entries in your vault when you create new accounts. You can also create "secure notes" storing things like your Wifi password, SSN, credit card numbers, insurance info, &c. Multiple types of multi-factor authentication are supported, including Google Authenticator, Yubikey (a USB stick with a keyfile), and a grid that you print off and carry in your wallet.
They've got a helpdesk with a bunch of FAQs and tutorial videos, etc.: https://helpdesk.lastpass.com/