What is the purpose of and what is stored on the iPhone 6s SIM card?

The SIM card is the link from the phone to your cellular provider.

In dumb phone days they could contain contacts and even sms these days they tie the IMEI of the phone to the contract with your carrier and nothing else really

Your sim card is what permits you to connect to your cellular network. All that is stored on the card is your cellular account information on iPhone. Things like contacts are not stored on a sim card on iPhone. None of the phone's data is stored on the card on iPhone. But without the sim card, you would not be able to make or receive phone calls.