It suggests that those states that are 'closed'/undemocratic/unfree (such as the Communist dictatorships of China and Cuba) are very stable; however, as one progresses right, along the x-axis, it is evident that stability (for relatively short period of time in the lengthy life of nations) decreases, creating a dip in the graph, until beginning to pick up again as the 'openness' of a state increases; at the other end of the graph to closed states are the open states of the West, such as the United States or the United Kingdom.
The text argues that countries with limited freedoms (like China and Cuba) tend to be stable over long periods. However, as these nations become more open and democratic, their stability decreases for a short time before improving again. The opposite is true for states like the US and UK, which are considered "open" and enjoy high levels of stability.