What is the purpose of litotes in the English language?
Politeness and ironic emphasis
Litotes is a deliberate understatement, usually saying that an object is "not" something.
Ex: "You don't look half bad"
(meaning, "You look good")
Ex: "He is not my favorite person"
(meaning, "He is my worst enemy")
Litotes can have several purposes. One is ironic emphasis: by drawing attention to a trait that an object is not you are pointing out a trait the object has.
Ex: "The president doesn't seem to be the kindest, most inclusive person." This points out how the president is unkind, and exclusive, and ironically may have a stronger effect that directly spelling it out.
Another everyday purpose might be politeness. Litotes is a good way to imply meaning without outright saying something rude.
Ex: "I'm not full yet, could I order something else?" This could mean, "I'm still hungry because you didn't order enough food", but in a toned-down, more polite way.