Quarterly means once a quarter (i.e. four times per year). The term is particularly used to indicate periodicals.

Many scientific and/or official publications appear on a quarterly basis:

• MIS quarterly
• Early childhood research quarterly
• Congressional Quarterly
• Political Science Quarterly
• ...etc

Resulting from this "scientific"/"official" connotation, using the name quarterly in the name of a magazine gives it a somewhat more uptight allure, as successfully exploited by e.g.:

• Gentlemen's Quarterly (even after it had become a monthly magazine, while still preserving a more "upscale" and "refined" perception than other men's magazines).
• Quarterly Essay (perceived as a highbrow magazine)