A sponsored tweet is an advertising tweet by which the owner of a Twitter account sells ad space by the way of a specific tweet delivered to all followers in his tweetfeed. The owner of the account endorse the advertiser’s message.
Theoritically, the advertising nature of the tweet must be pointed out by a specific mention "sponsored tweet".
A sponsored tweet must not be confused with a promoted tweet as it is the owner account which is paid and not Twitter and as only followers of the account are exposed.
An example of promoted tweet sold to Samsung by AP during the 2013 CES (the third in the feed).
When the sponsored tweet is sent by a celebrity, it is also called a Twitter endorsement