A Unique Definition
In one’s quest to try and explain the Trinity, the attempt is often followed by an analogy. Some may feel that none are suffice and will be happy to just say that it’s a mystery, that none can comprehend. Since the Trinity is unique in the universe (concerning one being in three persons) how could we make an accurate comparison anyways? Though I would agree that no one can fully understand God and his triunity of being, that doesn’t mean we can’t have any grasp of it at all. With prayer and study, I’m confident that God will give us the clarity we desire.
I have heard many of the various Trinity analogies out there and I’ll say that most are not accurately descriptive. In fact, some confuse people even more which is rather counterproductive. Many of us have heard the egg analogy where the shell, yoke, and white are all said to be God. The problem with this analogy is that they are compartmentalized and none of the three parts are the full essence or completeness of the egg. At best, this would be describing Tritheism. Another popular analogy is water, ice, and steam existing in different forms. Unless we are talking about the triple point of water, this analogy is describing Modalism.
There are many others out there that we could discuss, but I’d like to share my favorite one (which I feel is one of the best analogies) that I learned from a friend. Lets talk about the sun, ya that big bright object in the sky. The sun (God the Father) is the source of life. From it proceeds light photons/rays (God the Son) and from the rays proceeds the energy/heat (God the Holy Spirit). Now, the ray is not the sun itself but you can’t say it’s not the essence of the sun either, as it can’t be separated. The same can be said for the energy, it’s not the ray itself nor the sun, but it still is the same essence of both. So you have three parts of the one source which are distinct from each other but yet they are all one in essence.
Edit: The comments by Yeremyah brings up some valid points about the sun analogy and shows its weakness. Perhaps this analogy is not as strong as I previous thought. However, an analogy does not need to be an exact match to its comparison.  Gloria brought up a good one about space as well. If anyone else has any others that they would like to add to the list, feel free to put them in the comments section.
1. 2000 A Rulebook For Arguments pg. 35