Password managers don't solve all problems related to securing credentials. They do however, reduce many of the risks. There is no such thing as perfectly secure. But by reducing the vulnerabilities and weaknesses, you can improve your situation and greatly reduce the risks of loss.
For example, a password manager allows people to create different passwords, which are very strong, for different sites. One of the biggest risks is the repeated use of a single password across many different services. Although one password is convenient to remember, if an attacker finds out your password to one site, they can then login to many more. Your loss is therefore multiplied. There are other benefits, but I won't bore you unless you want more detail (I could write a blog on it if there was interest).