Litvishe is a Yiddish word, that refers to Haredi Jews, who are not Hasidim (and not Hardalim or Sephardic Haredim). The Hebrew form which is used with the same meaning is Lita'im. Other expressions are Yeshivishe and Misnagdim.
Both the words Litvishe and Lita'im are somewhat misleading, because there are also Hasidic Jews from Lithuania, and lots of Lithuanian Jews who are not Haredim. The reference to Lithuania does not refer to the country of that name today, but to the historic Grand Duchy of Lithuania, which also included all of modern-day Belarus and also parts of Ukraine. The term Misnagdim ("opponents"), on the other hand, is somewhat outdated, because the opposition between the two groups has lost much of its relevance.