Answer:
   
   A Jewish Marriage is one that has Kiddushin. This means that the
   husband and wife are sanctified to each other, and have an exclusive
   relationship. The Sanctification is under the Laws of Moses; thus,
   Kiddushin is only present (traditionally) if both parties are Jewish
   (and thus, only a marriage between two Jews would require a Jewish
   divorce).
   
   The Kiddushin relationship has legal ramifications. The marriage
   ceremony is one of acquisition. It is based on the rules for transfer
   of property in biblical times. In marriage, the woman accepts a ring
   (or something of value) from the man, accepting the terms of the
   marriage. A marriage contract (ketubah) is read publically. Witnesses
   are required for both the signing of the ketubah and the ceremony.
   Note: According to the Mishnah, a Jewish marriage is a legal contract
   and may be contracted in any of three ways: (1) with money (as when a
   man hands a woman an object of value for the purpose of contracted
   marriage, and in the presence of two witnesses, and she accepts); (2)
   through a written contract; (3) or by sexual intercourse, a method
   strongly discouraged by the Sages.
   
   Note the distinction between the Jewish marriage and the secular
   marriage. In the United States (and many other countries), when a
   rabbi officiates at a wedding, it is de facto a legal wedding by the
   law of the United States, as well; therefore, a rabbi cannot officiate
   for you without a civil license. This is the secular (civil) marriage.
   However, Kiddushin is a ceremony that takes place between two Jews.
   Most rabbis will not officiate at a wedding between a Jew and a
   non-Jew because it is outside the realm of Jewish traditional
   practice.