There are a couple of possible answers to the question of "What are Tinder scams?". I'll try to outline the most likely possibilities below:
Spam bots
Many people experience spam bots at some point of time on the internet, but they're a huge problem for dating sites as they know what the users are looking for.
The scam works by setting up a normal looking profile. It will usually contain an image of an attractive looking woman or man, and an appealing profile. Then the account waits for someone to make contact with the profile.
Once contact is made, the user will receive enticing messages from the profile, usually requesting that they click a link or join the person in a "private room". What is actually happening is that the user is being scammed into entering credit card information, which will then be used be the scammer.
Romantic Tinder scams
The second possibility is probably more hurtful, as the user is generally speaking to an actual person rather than a spam bot. This time, the person creates a profile, but uses someone else's image so as to not be tracked as easily.
Once contact has been made, the user will lured into a sense of security, often over a period of weeks or even months. After gaining the trust of the user, the scammer will then attempt to convince the user to send them money.
A common scam is of a fake soldier profile. The "solider" will spend a long time gaining the trust of the user, and will then say they desperately need money for something or another. As they're on "active duty" they can't get the money yet, but will pay them back. Of course, once the money have been received, the unfortunate user will never hear from them again.
How to avoid Tinder scams
If you're a member of a dating website, or indeed any site that involves talking to strangers, make sure you never provide any credit card or personal details over the internet. It might not be a scam, but more often than not, it will be.
Here's a video documenting the story of a dating website scam: