It means that it is on the same date every year.

In the US, for example, Independence Day is a fixed date holiday. It is always July 4th. Thanksgiving, on the other hand, is the fourth Thursday in November, so the date varies somewhat.

In this context, fixed means unchangeable, so it is the same day for all people in the country. You can imagine that there may be different groups of people who view the events of history differently, and thus choose different days to celebrate their country.