A baker is a job, in which a person makes bread as well as other baked goods and pastries to sell to people. In the poorer districts of Panem, few people can afford to buy the baker's products. It is mentioned that people from the Seam can't buy them most of the time.
Each district has its own style of bread. The style reflects the industry of that region. For example, District 4 has bread with seaweed in it because it is the fishing district. Another example, District 11 has bread that is in the shape of a crescent moon with seeds and/or grain on it because it is the district of agricultural crops. District 3 has small bite sized rolls, which may indicate the detail that people working with technology must pay attention to and the small computer parts which they design.
Bakers also make and design cakes, this is what Peeta did at his family's bakery which led him to excel at camouflage which was used as an advantage in the 74th Hunger Games arena when Peeta got injured by Cato. This resulted in Peeta camouflaging himself by a stream until Katniss Everdeen finds him after the announcement that two tributes can survive if they're both from the same district.
It is also mentioned that Katniss sometimes walked past the bakery with her sister Prim and admired the beautiful cakes, even though they could never afford them.