Once it was perhaps most commonly used to refer to speakers of Northeast Afroasiatic languages such as Arabic, Hebrew, or Amharic. The term Semitic used literally means pertaining to the descendants of Shem Noah's son who in Genesis 10:21 is called father of all Hebrews. However, with a few exceptions (most notably Hebrew), it is the people who are described in the Bible as the descendants of Ham's sons (Canaan & Put) who are considered linguistically Semitic. Thus the area of so-called Semitic languages is actually much larger than the area most people associate with the term "Semitic". They stretch all the way along the southern Mediterranean Sea to the Atlantic Ocean, into Mali and along the coast of the Red Sea all the way to Somalia in Africa. Semitic languages are also spoken in European Malta and on some islands in the Indian Ocean. Additionally, millions of Muslims speak Classical (Qur’ānic) Arabic as a second language, and many Jews all over the world speak Hebrew as a second language. It should be noted that Coptic, Berber, Somali, and many other related Afro-Asiatic languages within this area do not belong to the "Semitic" subgroup.
Hence the term's primary use these days is to refer to an ethnic group. The best modern way to test an ethnic group's common physical descent is through genetic research. Traditionally Jewishness can only be inherited from a Maternal line and though in genetic research no significant common mitachondrial results have been yielded, genetic Y-chromasome links between near-eastern peoples like the Palestinians, Syrians and ethnic Jews prooved fruitful. The indication is that these peoples do decend from a common Near-Eastern population which some have (perhaps thoughtlessly) applied the term semitic. .
Obviously over time the number of people to join Jewish communities, and marry descendants of the Israelites has not been trivial. But the results indicate that the male converts from outside descendants of that Near-eastern community has not been so large as to swamp the near-eastern Y-chromasome. Thus today's male Jews may be said to descend if not from the Israelites of Judah at least from communities in very close proximity to the original Israelites. See the article on Israelites for more detail.
Anti-Semitism is a term which the most common usage by far is to describe anti-Jewish statements or beliefs. However, it is increasingly used by people who apply the word in reference to Semitic people also in the linguistic and genetic senses.