The term "June 24" refers to the date, specifically the 24th day of the month of June. In English, we often refer to dates by naming the month followed by the day.
In some cultures, June 24 is celebrated for various reasons. For example, it is associated with Midsummer celebrations in some European countries, which mark the summer solstice.
In summary, "June 24" is simply a date but can carry different meanings depending on the cultural context.