Let me intervene right here, if I may. The "fist" is correct, also as a rough indicator of "martial art" or "boxing." But taiji or tai ji comes from Taoist cosmology. Metaphorically, it's about the creation of The Myriad Things (basically, the complex world) from an undifferentiated beginning. Remember, this is a metaphor that can be applied to many things.
In other words:
The universe started as wuji, which means "no extremes", "no opposites", "no polarities" or "no ultimates." Everything is the same, nothing stands out, nothing moves. This is represented by a circle.
The next state that arose was/is taiji, where stuff started happening. This is the constantly-flowing state of yin and yang: symbolized by the familiar black & white swirly image. Since this is the first time that stuff stood out (when opposites appeared), the taiji state can be translated as "grand extremes", "first extremes", "supreme opposites," "most important polarities," and so on.
So the meaning of ji as "ultimate" is not "best"; it's more like "opposite" or "polarity" or "end."
After taiji, yin and yang separate or become less fluid; then they combine in pairs, then trigrams to create the bagua, and onward. Metaphorically. :asian: