What are “mamzerim”?
It can be important to get a get for the sake of any offspring of a second marriage. If a Jewish woman remarries without having received a get, even if she has received a civil divorce, the children of her second marriage are technically considered mamzerim (illegitimate) and will not be accepted into many Jewish communities, Orthodox and otherwise. This means a mamzer cannot participate in a synagogue or marry a Jew either in an Orthodox community or in the State of Israel. If a man remarries without a get, his children are not considered mamzerim.
The Reform movement rejects the entire concept of mamzerim, and accepts any child of any Jewish parent as a Jew, able to marry into the community and participate in services. The Conservative movement holds the position that a congregation should not dig into a member’s background, which basically implies that a Conservative synagogue can turn a blind eye to the acceptance of mamzerim. In Orthodox circles, mamzerim are not permitted to participate in the religious life of the community in any way.
The status of a mamzer is inherited for ten generations. For this reason, even Reform, Reconstructionist, and unaffiliated Jews may want to get a get for the sake of their future children, grandchildren, and great-grandchildren, whose affiliation they cannot foresee. Though the Reform and Reconstructionist movements accept a civil divorce as sufficient to constitute a Jewish divorce, many liberal rabbis will counsel divorcing couples to get a get if possible in order to conform with a stricter interpretation of Jewish law. This is for the sake of any offspring of a second marriage.