A lot of people have difficulty understanding the Trinity, so I will give you the Orthodox rundown.
First off, the biggest issue people with the Trinity is that they don't see how it is meaningfully different from Tritheism (the heresy of three Gods). I will explain that do you: though the Father, the Son and the Holy Spirit are three distinct existences of God, they have one essence, will and action among them. Everything God does is From the Father, By the Son, and in the Holy Spirit. When you take an action, let's say, reading a book: the book comes from somewhere, and read is reading in somewhere else (like your room), but read BY you. Generally, you only do the by, the from, or the in. God does all three, he is completely self-sufficient.
Now, let's look at how the Son is begotten: this means, that the existence of the Son is eternal, but it is predicated upon the Father's existence, that is the Father furnishes the Son's existence, but he always has. The Spirit's existence is also furnished by the Father, in that the Spirit proceeds from the Father (he is channeled through the Son, but his existence is endowed from the Father). That means that the Father is the bedrock of the entire Trinity. In Roman Catholicism, God's essence is the bedrock, the principle of the Trinity; in Orthodoxy, the Father is the principle (so in a way, Orthodoxy is more existentialist, since the existence of the Father is principle, instead of the essence of the Trinity)
Each person of the Trinity is a distinct existence of one essence, sort of like how if you went back in time and met yourself, there would be two existences of you at the same time, but they'd both be you. Latin terminology would be three subsistences of one substance.