In her article "What is freedom" she says "The reason for this obscurity is that the phenomenon of freedom does not appear in the realm of thought at all, that neither freedom nor its opposite is experienced in the dialogue between me and myself..." what does this mean?
or Arendt, action is one of the fundamental categories of the human condition and constitutes the highest realization of the vita activa. [...] The two central features of action are freedom and plurality. By freedom Arendt does not mean the ability to choose among a set of possible alternatives (the freedom of choice so dear to the liberal tradition) [emphasis added] or the faculty of liberum arbitrium which, according to Christian doctrine, was given to us by God. Rather, by freedom Arendt means the capacity to begin, to start something new, to do the unexpected, with which all human beings are endowed by virtue of being born. Action as the realization of freedom is therefore rooted in natality, in the fact that each birth represents a new beginning and the introduction of novelty in the world.
Thus, freedom is not grounded in rationality: "freedom does not appear in the realm of thought".
It is something "deep", grounded in our inner original self.
From the context in What is Freedom we can see, that by the obscurity of freedom Arendt is meaning that the ocurrence of freedom cannot be proved -or disproved- empirically, that is through observation. In addition, she is endorsing two further theses of Kant on freedom. First, that freedom cannot be ascertained by subjective "inner" experience, not just by "outer" sense experience. Second, that if we ignore the inherent limitations of our ability to know, we must end up in logical contradiction - antinomy - because then both freedom and its opposite, determinism, can be proved to be the case.
The greatest clarification in these obscure matters we owe to Kant and to his insight that freedom is no more ascertainable to the inner sense and within the field of inner experience than it is to the senses with which we know and understand the world. Whether or not causality is operative in the household of nature and the mind to bring order into universe, it certainly is a category of the all sensory data, whatever their nature may be, and thus it makes experience possible. Hence the antinomy between practical freedom and theoretical non-freedom, both equally axiomatic in their respective fields, does not merely concern a dichotomy between science and ethics, but lies in everyday life experiences from which both ethics and science take their respective points of departure.