If people promote something, they help or encourage it to happen, increase, or spread.

If a firm promotes a product, it tries to increase the sales or popularity of that product.

If someone is promoted, they are given a more important job or rank in the organization that they work for.

If a team that competes in a league is promoted, it starts competing in a higher division in the next season because it was one of the most successful teams in the lower division.