Medium is a platform for writers to collaborate and publish their works to a range of users. Using their API you can access details about Users, Publications, Posts, and Images.
In order to publish on behalf of a Medium account, you will need an access token. An access token grants limited access to a user’s account. We offer two ways to acquire an access token: browser-based OAuth authentication, and self-issued access tokens.
Unless there is a compelling reason, you should use browser-based authentication.
The terms of service can be found here https://medium.com/@Medium/medium-api-terms-of-use-2b405a832a2f#.n9ygqgq5q