How does a password manager (password vault) solve the "many strong unique passwords" problem?

Question

Accepted Answer

It generates and stores a different strong password for every service, so you only have to remember one master password.
The core tension: best practice demands a long, unique, random password per service — but humans can't remember dozens of those. A password vault (e.g. KeePass, 1Password, Password Safe, SecureSafe) resolves it by:

generating strong random passwords for you
storing them encrypted behind one master password
autofilling them so you never have to type or recall them

Why this is the practical answer: it makes "unique password per service" actually achievable. Without a manager, people reuse passwords precisely because remembering unique ones is impossible.
Tip: Some managers integrate breach checks (e.g. against Have I Been Pwned) to warn you when a stored password appears in a leak. Protect the master password well — it's the one key to the vault.