A zivug is a life partner. In modern Hebrew today ben or bat zug is the politically correct term for ones significant other, equivalent to partner in English.
The word has some surprising connections to contemporary English via a common Greek root. Zivug comes from the Greek zogen, meaning to join and zeugen, a pair. This comes from the same source as zygote, which, means a complex cell generated by the sexual reproduction of two gametes. According to the invaluable Jewish-words blog balashon, these derive from the Indo-European root yeug, meaning to join, from which we have the words conjugal, jugular, yoke and even yoga, which means union.
The etymology tells us that a zivug is not just a life partner. It also has the sense of being the right life partner. The rabbis were under no illusions about how difficult the search for a zivug can be can be. The Talmud (Sotah 2a) writes that it is as hard (for God) to make zivugim as to split the Red Sea. Another source says that since creating the world, matching zivugim has been Gods principal occupation. On the one hand, the rabbis did express the sense of miraculousness about finding ones predestined other half. (Forty days before birth, a heavenly voice goes out and says, This persons son is for that persons daughter.) Yet they are aware, too, of the complexities of the quest for a mate; of first marriages and second marriages and missed opportunities, and how, nevertheless, one may find the right one, through whatever unfathomable means.