Other parts of the SEP holds at least some keys to your question:
Her name has been invoked by a number of critics of the liberal tradition... There are many strands of Arendt's thought that could justify such a claim, in particular, her critique of representative democracy, her stress on civic engagement and political deliberation, her separation of morality from politics, and her praise of the revolutionary tradition.
and hence her celebration of
the American Revolution, because there the act of foundation took the form of a constitution of liberty. Her other examples are the revolutionary clubs of the French Revolution, the Paris Commune of 1871, the creation of Soviets during the Russian Revolution, the French Resistance to Hitler in the Second World War, and the Hungarian revolt of 1956.
Further, she calls
Action, the only activity that goes on directly between men without the intermediary of things or matter, corresponds to the human condition of plurality.
action as a mode of human togetherness, Arendt is able to develop a conception of participatory democracy which stands in direct contrast to the bureaucratized and elitist forms of politics so characteristic of the modern epoch.
By participatory politics shes looking back to the origin of democracy in the greek polis, and this part of her act of interpretation (hermeneutics) of the political tradition in light of the various forms of totalitarianism evident in the early 20C by going back to the originary myth of Athenian Democracy, and reinterpreting not as representative democracy but refocusing on the genuinineness, authenticity and directness of participatory democracy.
Finally Action is not action as in action-movie or actioniste art; Arendt
stresses repeatedly that action is primarily symbolic in character and that the web of human relationships is sustained by communicative interaction
We may formulate it as follows. Action entails speech: by means of language we are able to articulate the meaning of our actions and to coordinate the actions of a plurality of agents.
So Arendt is rescuing the ancient art of rhetoric, the art by which politics acts by persuasion, and that Plato denounced in favour of the art of contemplation.