Where English has yes and no, Icelandic has já, jú and nei. Both já and jú translate as yes, but there is a distinct difference between how the two are used. Já answers affirmative questions, while jú answers negative questions. In grammar, a negative question is any question with the word not or similar: it has nothing to do with subjective qualities like positivity and negativity.
In addition to answering negative questions, jú can also be used to contradict a (grammatically) negative statement.
Note the disambiguation provided by using two different forms for affirmation. The examples below sound perfectly natural in Icelandic, but in the English version a clarification is almost obligatory.
Aldrei can also be used to formulate a negative question.
Víst can be thought of as a stronger version of jú, when used to contradict a (grammatically) negative statement. It cannot be used to answer negative questions. The closest thing to a proper translation in English might be the exclamation point: body language and vocal inflection would convey the difference in spoken language.
Víst is an adverb, so in neutral word order it comes after the verb and subject. If it is fronted (brought to the front of the sentence for emphasis), the subject and verb are inverted.
Many a playground argument has devolved into an exchange of nei and víst.