We have learned that a husband can be mefer – nullify – a neder made by his wife. The Mishna on our daf discusses whether his brother, the yavam, can play that role in the event that he dies without children (see the introduction to Massekhet Yevamot for an explanation of the rules of yibum.) The Mishna teaches that this is a disagreement among the tannaim, and the Gemara explains that the focus of the disagreement is whether the concept of zika – a substantial bond – is accepted or not.
The word zika is a noun that expresses a theoretical relationship or connection, which – in its original meaning – indicates that one person is tied to another in some way. In modern Hebrew, for example, the word azikim means handcuffs or restraints. The Sages used the term less for its literal meaning and more to express a legal or emotional tie between people.
According to the opinion that zika does not exist, the relationship between the yavam and the yevama is that described in the Torah – the widow cannot marry out of the immediate family without undergoing the ceremony of halitza. According to those who believe that zika exists, however, we view the yavam and yevama as being engaged, and possibly to actually be married with regard to certain halakhot.
The Gemara in Massekhet Yevamot (18a) suggests that according to Rav Yehuda the zika is so strong that even if the woman dies, the potential yavam will not be allowed to marry her relatives, since we view it as though there was a relationship between them that was similar to marriage. The Talmud Yerushalmi, however, brings an opinion that even if you accept the concept of zika, in the event that the yevama dies, it becomes clear that the yibum relationship is never completed and the zika is retroactively annulled. Thus the surviving yavam would be permitted to marry the dead woman’s relatives.