It's used for all sorts of "prove you are who you are" situations. It's most commonly associated with applying for credit/loans, and taxes, but definitely not limited to those things. It's ridiculous that an immutable 8-digit number + name is used for authentication in the USA. It even says on the card "FOR SOCIAL SECURITY AND TAX PURPOSES - NOT FOR IDENTIFICATION" but apparently we've all lost our minds and ignore that. It can be very difficult to go through business processes if you refuse to give your SSN - some healthcare providers will just refuse to serve you.

With it, people can take out loans in your name, get into your accounts, file fake tax returns and get tax refunds in your name, and generally act as if they're you. Things are getting a little better nowadays (with additional information required) but we still don't have a secure method of identification online / over the phone.

Over here we use a PKI cert for that. A smartcard providing the root of that trust is provided by the government after verifying your identity using the typical stuff used for identity documents (any biometric data on file, birth certificate, etc.). That still doesn't mean that it's impossible to steal an identity, or acquire a made up one, but it does make it a whole lot harder.