A password manager allows you to set extremely complicated passwords that are unique for every site. If left to a human brain, we would most likely reuse or use a variation of similar passwords since there is a limit to how much we can remember. Remembering one very complex master password is easier than remembering many complex passwords for different sites.
There are online and offline password managers. An online password manager is a service provided by a company and they are more vulnerable to cracking. An offline password manager is safer because the database is stored locally on your computer. Before an adversary can even crack the password, he needs to have access to your computer first.