The most often asked question to a Christian
What is this Trinity?

To begin to understand the Trinity, one must first understand that the holy Bible is the Word of God. It is not a book written by men about God; but a book written by God.  The Bible is not a book by men seeking a lost God; but a book by God seeking lost men.

To understand the Trinity, let's begin with "basics" by reviewing what Jesus told us in the holy Bible.  Jesus told us "God is Spirit".  Nobody can yet describe accurately just what a spirit is, so let's just say what we do know.  It is not flesh and blood.  So the "rules for a spirit, its limits, nature and capabilities" are likely much different from those of  mortal beings.  As to a human ever really understanding the nature of the Most High God;  ask yourself, can a dog know the nature of a man?

No Christian (including Catholic priests and mainline Protestant Ministers) believes there are "three gods in one". 

Christians believe there are 3 persons, all having the same substance.  These 3 persons are infinitely coexistent, coeternal, and coequal.  They each have their own "natures". For evidence of this we look to the holy Bible and scripture.
 

Remember, when Jesus was being baptized by John the Baptist, the Father's voice was heard to say; "this is my Son".  Also present was the Holy Spirit. See Matthew 3:16-17.

The plurality of God is is also demonstrated in Genesis 1:26 where Jehovah says; "Let us make man in our image, after our likeness."  It's obvious God is not talking to angels here.  Since we know from Isaiah 43:10-11 that there is not any God other than Jehovah (aka: Yahweh, I Am, Yeshua/Jesus), then Jehovah is talking to the Son and the Holy Spirit --who are equal in substance to Jehovah.  This plurality is repeated in Scripture often enough.  For instance at the Tower of Babel Jehovah says in Genesis 11:7, "let us go down, and there confound their language."

Psalm 45 & Hebrews 1 speaks of this "plurality" also:
 

And what did Jesus say of this Triune God?  In Matthew 28:19 we know that Jesus said; "Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost. 

Jesus is another "Comforter", just like and equal to the Holy Spirit.  In John 14:16, we are told by John that Jesus said; "And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever."  Jesus told us all we need to know, when He told us: I and my Father are one John 10:30.  Speaking of Jesus in Colossians 2:9 we read: "For in him dwelleth all the fullness of the Godhead bodily." And, Jesus knows in advance what the Father "shall" do.

Something that is very germane to this discussion is that Jesus performed miracles in His own name.  And Jesus forgave sins in His own name.

And what power did Jesus have to call on the other two (Father & Holy Spirit)?  In John 15:26 Jesus said: "But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me."  Why did Jesus have this power?  Jesus answered this while speaking to His apostles.  And Jesus came and spake unto them, saying, "All power is given unto me in heaven and in earth." Matthew 28:18

What happened before Jesus became incarnate?  In Luke 1:35 we read: "And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God."

So what is God?  God is an awesome, infinite, loving Spirit and light.  God is incapable of lying or sinning.  Therefore we can thoroughly believe that those who repent and place their Faith in the Lord Jesus will merit eternal Life.  Because Jesus who is God also told us so.

And how do we know for certain there is a Son nature of God?

As graphic examples, try to imagine 3 flashlight beams aimed at the same spot.  All 3 have different natures, yet all merge as One and the same.   See the light of the Father and the light of Jesus being one and the same in this true Near Death Experience. 

See scriptural references as Jesus being God, including Thomas saying; "My Lord and my God" to Jesus. See here

Jesus fulfilled over 350 prophecies about Himself. Of these, over 105 it would be impossible for anyone else in history to fulfill. Figure the odds. See here

Historic document from Clement helps us with the Trinity:

Note how Irenaeus' passage below gives us an inkling of why we should pay attention to Church Tradition. When he speaks of Clement - he tells us that even Clement who was the 3rd head bishop from the apostles --had listened to and spoken to the apostles. According to Tertullian, writing in about 199 A.D., the Roman Church claimed that Clement was ordained by Peter himself (De Praescript., xxxii). Most Catholics think of Clement as the 4th Pope. Clement did leave us a writing of his. It was a letter to the Church at Corinth. See some of this far below...

The passage by Irenaeus (Adv. haereses, III, iii, 3) reads:

"The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate. Of this Linus, Paul makes mention in the Epistles to Timothy. To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric. This man, as he had seen the blessed apostles, and had been conversant with them, might be said to have the preaching of the apostles still echoing [in his ears], and their traditions before his eyes.


From Clement's letter to the Church at Corinth:

A passage on the Holy Trinity is important. Clement uses the Old Testament affirmation "The Lord liveth", substituting the Trinity thus: "As God liveth, and the Lord Jesus Christ liveth and the Holy Spirit -- the faith and hope of the elect, so surely he that performeth", etc.

Holy Spirit is distinguished/separate here:
 

Reference on Clement: here

Follow the discussion of this at the Bible Talk Message Board: here