Sexagesima Sunday is the second Sunday before the start of Lent, which makes it the eighth Sunday before Easter. Traditionally, it was the second of three Sundays (Septuagesima is the first and Quinquagesima is the third) of preparation for Lent.
Sexagesima literally means "sixtieth," though it only falls 56 days before Easter. It most likely takes its name from Quinquagesima Sunday, which is 49 days before Easter, or 50 if you count Easter itself.
When the Roman Catholic liturgical calendar was revised in 1969, the three pre-Lenten Sundays were removed; they are now denominated simply as Sundays in Ordinary Time. Septuagesima, Sexagesima, and Quinquagesima are all still observed in the celebration of the traditional Latin Mass. (Read entire post.)