初 is used as a prefix for 'initial/beginning': 初级 (beginner level), 初步 (preliminary), 初恋 (first love). In dates, 月初 means 'beginning of the month', 年初 means 'beginning of the year'.
culture
In the lunar calendar, 初一 to 初十 are the first ten days of each month. 正月初一 is Chinese New Year's Day.