I'm a bit new to this topic myself, but your question is also a bit unclear. If you mean the consumer key tokens that are used in oAuth systems, these are required to ensure that the third-party using your API has actually been granted access to use it - anyone without a consumer key cannot use your API.
Alternatively, if you are referring to users being authenticated using an authentication token...
When you create a rails app that has authentication (for example using the devise gem) a sessions controller is also created/used. Sessions(/cookies) are basically a way of 'remembering' that the user has logged in. This avoids having to resend username/password with every action the user performs in order to authenticate him/her for that action.
This approach works perfectly fine when it comes to web apps because all browsers support cookies. However, this is not true when it comes to mobile apps. It is not possible to keep a session/cookies when using a native app (well it is technically possible, but from what I've read it seems to require quite a bit of manual labor and a bit of code wizardry to get it working correctly).
Now, when you create an API for your app, you need to bear in mind that your API may be used for creating a mobile app (either by you in the future or if you open it to the public). This means that using sessions probably isn't a good idea. For each request that requires authorization the username/password will need to be sent to ensure the user has access to perform the requested action. But sending username/password with each request is definitely a bad idea. That's where token authentication comes in. If you've ever used devise, you will notice there is an option to enable token authentication. This basically allows the 3rd party to send a token rather than the username/password and works just the same. The good thing about this approach is that even if a token gets stolen they can expire and a new one can be generated without the user even realising and without the users password being stolen.
(I'm fairly new to the topic myself, from what I've gathered so far that seems to be how things work. Now if I have made any mistakes in my explanation/understanding I hope people will jump in an correct me.)