Organs of government propaganda are the means by which government disseminates its propaganda, meaning methods of communication designed to persuade people to its stance or point of view. "Propaganda" is perceived almost universally as a negative term, but what is or is not propaganda depends largely on one's perspective, as a few examples should make clear. There are many "organs" of propaganda, and governments at one time or another have taken advantage of all of them.
Two common organs of government propaganda are television and radio. In some countries, these are actually owned and operated by the government, and viewers and listeners are subject to whatever the government wants them to hear, all promoting that government's agenda. I imagine that North Korea, for instance, has no television or radio station that is not government owned. And there are other countries in which the television and radio stations are not owned and operated by the government, but are subject to strict government control and forced to air ads or other content that promotes the government's agenda.
Newspapers can be state-owned or controlled as well, in a similar fashion. And even in a society with a free press, newspapers can be organs of government propaganda. For example, if the administration wishes to garner support for its doings, it will often "plant" stories in newspapers, which the newspapers have a tendency to go along with, possibly as a quid pro quo for gaining more cooperation from the government in interviews.
Another organ is the pamphlet drop. During World War II, the United States dropped thousands of pamphlets to people in Europe and in the Pacific front, to persuade them of the United States' point of view and efforts in the war. These were always in the language of the people whom the drops were aimed at. My father brought home a number of these from the war, in German and in French.
I would say that generally, governments that are repressive tend not to use social media such as Facebook to communicate propaganda because these are governments that can ill-afford to allow their citizens to use such social media. This would allow citizens to see other perspectives and thus ruin the value of the propaganda.
In short, any way that a government can communicate with people to persuade people of its point of view can be viewed as an organ of government propaganda. Whether one thinks that communication is propaganda or simply friendly information depends on one's perspective.