Nusach Ari means, in a general sense, any prayer rite following the usages of Rabbi Isaac Luria, the AriZal, in the 16th century, and, more particularly, the version of it used by Chabad Hasidim.
In 1803, Rabbi Schneur Zalman of Liadi, the founder of Chabad Hasidism, published a prayer book that was arranged according to Nusach HaAri. This prayer rite has been used ever since by Chabad Hasidim.
Read more about Nusach Ari: History of The Siddur, Siddurim Adapted From The AriZal's Siddur, See Also