Propaganda shots, more commonly known as propos, were the advertisements, messages, interviews, and footage from the rebel side (although the Capitol had a few propos as well) and were part of the Airtime Assault on the Capitol. Propos communicated messages to Panem's citizens, giving statements against the Capitol, and provided a rallying point of sorts for the rebel war effort.
The nature of propos implies that the word was a take on the word "propaganda," meaning information, ideas, or rumors that are deliberately spread widely to help or harm a person, group, movement, institution, nation, etc. Katniss Everdeen's condition and realities behind the war were some of the main focuses of propos. Chapter Three defines propos as 'propaganda spots'.
Beetee was in charge of getting the propos to air in the Capitol by breaking through its broadcasting system. He was able to do so multiple times by essentially redesigning the underground network that transmits all programming.
Propos in the rebellion
One propo was used as a distraction during the rescuing of Peeta, Johanna, Annie Cresta and Enobaria from the Capitol. It featured Katniss revealing how she met Peeta and their exchange with the bread. It also showed Finnick Odair revealing all the secrets he had collected over the years about prominent people in the Capitol, including President Snow's serious offenses.
Fulvia Cardew came up with the idea to run a series of propos narrated by Finnick that paid tribute to the memory of past tributes from each of the districts, the theme being "We Remember." It was an effort to reach out to any people in the districts who were still unwilling to join the rebellion.
Another propo was the propo showing Finnick and Annie getting married. The propo was made more for entertainment than propaganda.