Oosquai is a particularly potent alcoholic drink made and consumed by the Aiel. Made from zemai, (maize) it looks "like faintly brown-tinged water, tasted almost like it — and was stronger than double-distilled brandy" according to Rand al'Thor.
Aviendha, Min Farshaw, and Birgitte Silverbow all drink a heavy amount of oosquai while Rand and Elayne are making love for the first time in order to numb the sensations they are feeling through their bonds to either of the individuals.
The sharing of oosquai with another person is said to be a great act of friendship between warriors.
In our world, we would call it whiskey. This is supported by the word zemai reading as maize (or corn) with the phonemes reversed; corn is one of the grains that can be used to make whiskey.
The name is likely based on a Gaelic word for whiskey: uisce beatha. Robert Jordan has stated in interviews that he based some cultural characteristics of his characters on the ancient Celtic culture. He likely was referring to the Aiel.
'In English whiskey is derived from the Gaelic word 'uisge beatha' which means 'water of life'. This, in turn, is attributed to a translation from the Latin aqua vitae by Irish monks of the early Middle Ages. Aqua vitae was the name for alcoholic liquors distilled by ancient Romans.