Thomist philosophy held that essence preceded existence, apart from God whose essence was existence; and this in line with a conception of God as the necessary being; whereas humans and all else are contingent.
Mans essence being his soul; one can say that being in the world existence draws out his essence; in a similar way that in Platos a Dialogue The Theatatus; Socrates draws out what in essence was already there.
An old tradition stated that through introspection one can discover the hidden divine realm; consider for example in the Islamic tradition Al-Hallajs utterance Ana al-Haq (I am the truth - truth being a name of God - for which he was executed) which has parallels in the Christian and Indian traditions.
But after the death-of-god theology of Nietzsche; this realm evaporated so as Haydon explains that when Sartre looked within and 'pushing aside memory, knowledge and sensation' he found nothing; and he turned this into the philosophical concept of Nothingness.
Sartres innovation is to turn turn the two terms around so that existence precedes essence; one exists first and it is through existing in the world and it's commitments that's ones essence is formed.
Thus all there is is the material and the empirical; and when one pushes this aside, one does not find God as 'hidden treasure' or a 'lamp in a niche'; or as for Kant the 'moral law' but nothing, the void - a blankness.
This induces nausea and vertigo.
We have only the pure thingness of things rather than being imbued with something more than they are; there is no presence, just absence - or one could say the presence of absence.
The non-rational is not the lack of thinking or of thought as such; but should be seen as a term placed in opposition to the Enlightments project of rationalism; hence the reactions of Romanticism and Existentialisms.
As Haydon points out there is a kind of a parallel in the traditions of the East; possibly in particular the Tao, whose opening lines echo that of Sartres philosophical opus Being & Nothingness.