This symbol is intended to be a visual depiction of the Doctrine of the Trinity. This doctrine states that God is three persons, but one substance. The three persons of the Trinity are historically designated as the Father, the Son, and the Holy Spirit.
According to this doctrine, each person is distinct from the others, yet all three are one substance. This shield attempts to portray this complicated doctrine graphically.
The three "bubbles" on the outside represent the distinct persons in Latin - Pater - Father, Filius - Son, Spiritus Sanctus - Holy Spirit. Between each distinct person we find the words "non est" or "is not."
The central "bubble" represents the unity, or single substance of deity, "Deus." Connecting each distinct person with the central substance we find the word "est" or "is." So in other words, the Son is not the Father, but the Son is God, and the Father is God.
The shield is an attempt to portray in art something that confounds our logic
In my experience, the Trinity Shield is somewhat rare. This may be due to its limitations. For example, while attempting to depict the trinity, the shield actually presents what appear to be four entities. Further, this image emphasizes "three" over "one," both limitations could easily draw fire from ornery theologians.
There is no theological explanation of the Trinity in scripture. Nonetheless, we look to a number of passages as Trinitarian in their depiction of God. For example, read Mark 1.9-10. In this passage we see the baptism of Jesus, the Holy Spirit appearing as a dove, and a voice coming from above, often assumed to be the voice of God the Father.
Next, read John 14, in which Jesus discusses both the Father and the Spirit.
After reading these passages, reflect on the Trinity shield. How does it reflect the Trinity as found in these verses? How does it reflect your understanding of God as three yet one?
The trinity shield opens a wonderful avenue to preaching the Trinity. It highlights the ways we try to understand this complex doctrine, and also demonstrates how difficult it is to "explain" something that is so illogical.
In preaching with this symbol, you could highlight its shortcomings or its strengths. You could also explain your own Trinitarian theology. It may also be worthwhile to point out the role of faith in understanding doctrines like this as opposed to reason alone.
The most obvious time to use this image would be on Trinity Sunday. Another option would be when celebrating the Baptism of Christ, which for some traditions is around the time of Epiphany.