Honest question. What do people do with these besides buy and sell them?
Purchase other cryptocurrency coins and tokens - most are only traded against BTC (some against ETH), very few with currencies like USD.
Other than that, it's just a commodity like gold - it does nothing, but people treat it like it has value - albeit one that has extreme price fluctuations.
I think it's still important to distinguish between a commodity like bitcoin with the smart contract decentralized applications built with blockchain that have led to an entirely new industry these past couple of years, for people who think this entire space is pure speculation. It's all very very new, and I had no idea about this myself until googling it earlier this year, I think it's really exciting!
Applications and services with issued tokens have a value, but that value (though certainly dependent mostly on speculation at present) theoretically should be derived from real world use, e.g OmiseGO, a payment processor in Thailand. Omise will be launching an app that will let people spend any currency they want seamlessly, like Bitcoin for McDonalds, or Starbucks points at the supermarket. They recently announced a partnership with McDonalds Thailand that caused the price to boom (right now, they're just a payment processor like Apple Pay - the OmiseGO cross-currency function will be implemented next year). They've issued tokens used to facilitate the running of this upcoming service, and once it's fully operational there will be routine payments of a portion of the overall transaction fee to holders of the token. So, the more the network grows, the more the token should hypothetically be worth, since it will generate a passive income to its holders. There are only a fixed number of tokens - no more will be created.
The initial price of OmiseGO tokens for early investors was 0.24 cents, about double that when it first listed on exchanges this past summer. It's currently valued at $8.50 per token, with a market cap of over $800million.
So there are essentially hundreds of startups like this using blockchain tech and their own tokens. I'm sure most will fail (maybe OmiseGo will fail!), but for those that don't...