The symbol in my new banner

This object is called a Triskele. It has its origins in neolithic Europe, and is mainly accredited to the neolithic people of Ireland (pre-Celt). Its use spread to Macedonia (in modern-day Greece) and Sicily (part of modern-day Italy), and even Korea. Unfortunately, the original meaning of the symbol has been lost.

It's possible that the three sides represented three seasons: wet, dry, cold (or a variant on the theme). It may also have represented the three trimesters of human pregnancy. Given these two possibilities, it might have been an early form of a calendar, in my opinion.

In modern times the triskele symbolizes a group of three. The user may select whatever trio is special to them. Christians might select God, Jesus and the Holy Ghost. Wiccans might select the three stages of the Goddess (Maiden, Mother, Crone), which some refer to as the Triple Goddess.