In Judaism eight represents a new beginning. After the first seven days of a boy’s life, the b’rit takes place on the eighth day. After the seven days of Sukkot, Sh’mini Atzeret is the culminating chag of the festival month.
In the messianic age the Temple service will be accompanied by a harp of eight strings whereas until then the harp will have seven strings.
Each example is of a new beginning. The first seven of anything lays the foundation: thereafter we move into a new era.
Is there any connection with the saying, “the seven-year itch”?
In terms of marriage some people possibly think that after the first seven years either or both of the couple are itching for a new partner, a new attraction. This notion bodes ill for the marriage. The better approach is to use the eighth year not to get out of the marriage but to get more deeply into it.