In Jewish tradition, the number seven is associated with perfection. We have 7 days of creation; Shabbat is on day 7; there are 7 weeks between Pessah and Shavuoth; 7 years in the sabbatical cycle; 7 cycles of 7 years in the jubilee cycle; 7 days of Pessah and Succoth by biblical rule.
But what is the significance of 8? What comes after the holiness and perfection symbolized by 7?
This question is especially relevant in relation to the festival of Shemini Hag Atsereth--the 8th day closing festival. No other festival day in the Torah is tied to the number 8.