Tessera (plural: tesserae) are tokens worth a very meager year's supply of grain and oil for one person.
The option to receive tesserae is available in the districts of Panem to children between the ages of 12 to 18 (those eligible to participate in the Hunger Games). If their family is struggling for food, they can have their name added additional times to the reaping, once only per family member, in exchange for an equal number of tesserae. Once this is done, they can collect oil and grain rations once every month for a year. This, however, is not enough to survive by as many still require money for basic needs such as rent, soap, thread, and candles. Tesserae entries are cumulative, therefore the number of reaping entries from the current year are carried over into the next.
The practice of exchanging reaping entries for tesserae is especially common in the poorer districts such as districts 10, 11 and 12, while far less common in richer districts such as districts 1, 2 and 3. The largest gap is between districts 1 and 12, with nearly a 1:800 ratio, respectively.
Characters taking tesserae
The series' main character, Katniss Everdeen of District 12, has taken tesserae for each of the 3 members of her family (herself, her mother, and her sister) every year since she turned 12. This has given her three extra entries in the reaping per year, with a total of 20 by the time of the reaping for the 74th Hunger Games, at age 16. At the same reaping, Katniss's friend, Gale Hawthorne, age 18, had a total of 42 tesserae entries: one for each of the 5 members of his family (Rory, Posy, Vick and his mother). It is likely that many if not most of the Seam children take out tesserae at some point or another.