Promote Mode is primarily a mobile feature users can readily access through the Twitter app's menu drawer. It's where they can see all the numbers that matter, including how many followers they've gained and the number of people who saw their tweets and visited their profiles. On desktop, users can access the feature and those metrics through social media software Sprout Social.
Despite providing an automated way to promote tweets, the feature's success all depends on the subscribers' activities. Their tweets still need to be good, informative or witty enough to able to convince people to hit the Follow button. Unfortunately, even the most interesting accounts can't access the feature yet if they're not in the US or the UK. It's only out as a public beta in those locations, though it will also come out in Japan in the near future.
From the time Twitter first introduced the feature, it was pretty obvious that the company conjured it up as a new way to make money. According to its Q3 earnings report, it just had one of the best quarters (if not the best quarter ever) after managing to trim down losses to $21 million. If the feature does well, it could even help the company finally turn a profit.