According to Twitter, “Moving forward, we may use these labels and warning messages to provide additional explanations or clarifications in situations where the risks of harm associated with a Tweet are less severe but where people may still be confused or misled by the content. This will make it easier to find facts and make informed decisions about what people see on Twitter.”
Twitter will choose between either applying labels to tweets or for more severe misleading claims, will add a warning before the tweet can be displayed (similar to how Twitter warns users of NSFW content). Labels will also contain a link to a Twitter-curated page or an external trusted source that will provide users with additional and perhaps more accurate information about the claims made in said tweet.
In more severe cases with regards to misleading claims, Twitter states that they might even outright remove the tweet. According to Twitter, “Serving the public conversation remains our overarching mission, and we’ll keep working to build tools and offer context so that people can find credible and authentic information on Twitter.”