You login to pretty much all government services and a lot of private ones using it. In Sweden if you have BankID you can:
- login to the national healthcare service (1177.se) and see your medical records and all drugs that have ever been prescribed to you (although it is not 100% coverage on all healthcare practitioners yet)
- Open a bank account in a lot (most?) banks in a couple of minutes online
- Login to the tax agency and do your tax declaration (which is usually just pressing "Send" for most people)
- Login to the state pension fund and move your pension from one pension provider to another. As well as login to any of the pension providers to allocate your pension on funds you chose
- Authorize credit card purchases (using 3-D Secure)
- Login to the Metro company to attach your metro card to your ID in case you lose it
- A bunch of other things
But yeah, if you don't have this BankID system (which requires a bank account and thus an ID-number/ID-card and thus residency in sweden) it is a nightmare. Affects everyone who moves into Sweden, it can take quite some time to have all the pre-requisites to get BankID.