If you work for a marketing firm, your job is to promote new products — to publicize them and to try to get the public to buy them.
The verb promote can also mean to advance to a higher position. Because of your hard work, your boss might decide to promote you. In school, passing students are promoted each year when they enter a higher grade. In chess, the verb promote is used when a pawn is exchanged for a higher ranking piece. Make sure you promote your pawn to a queen, giving you two queens on the board and a strong advantage in the game.