Twitter has allows several promoted things:
A promoted tweet is a post on Twitter that the author has chosen to pay Twitter to show in various places on Twitter that it either would not otherwise be displayed (like a stream of followings tweets), or be given preferential display treatment, such as the top of some search results.
A promoted account is similar to a promoted tweet in that a (the latest?) tweet from an account is shown in places it would not otherwise be shown, or is given preferential display.
E.g. in followings stream:
The tweet above from @JohnLegere appears to be a promoted tweet, however the addition of the explicit full name near the promoted icon and text in the lower left and Follow button in the lower right all underneath a horizontal rule below the tweet itself but still in the box containing the tweet indicate that it is a promoted account.
Also in who to follow box: