The Junior Anti-Sex League in 1984 is a group that advocates "complete celibacy for both sexes." They are pushing the agenda of the Party, the group that rules the country.
According to the Junior Anti-Sex League, children should not be conceived through sexual intercourse. They should be conceived from artificial insemination only. While the Party in 1984 is moving away from standard sexual procreation, it has not dropped it entirely yet. It just makes sure people are in marriages that are planned to be unsatisfying and that sex is vilified.
The group puts up posters, hands out pamphlets, and holds rallies to push its ideas on the population.
When Winston thinks of Julia, he notices the "narrow scarlet sash, emblem of the Junior Anti-Sex League" around her waist and says it is just tight "enough to bring out the shapeliness of her hips." He later finds out that she doesn't actually believe in the group's rhetoric. She only joined to appear like she did.