The concept of the Trinity is, simply, one which correlates the fact that the Father, the Son (Jesus), and the Holy Spirit are all referred to as God in the scriptures ...
Father —
Galatians 1:1
Son —
John 1:1, John 20:28
Spirit —
Acts 5:3-4
... with the Bible's concurrent declaration ... that God is One God.
For instance, the Bible contains numerous clear statements regarding the unity of God:
Deuteronomy 6:4 tells us that "the Lord is one."
1 Corinthians 8:4 adds that "there is no God but one."
1 Timothy 2:5 explicitly says "there is one God." All Christians heartily affirm this truth.
However, the Bible also contains clear statements regarding diversity within that unity. For instance, in the very first verse of the Bible we are told that "In the beginning God." The Hebrew word for God is elohim, which is actually a plural form of the word el. It's a word that in other contexts is sometimes translated as "gods," referring to heathen deities. Later in the same chapter we have one of the most striking statements of diversity-in-unity:
Then God said, ‘‘Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground." So God created man in his own image, in the image of God he created him; male and female he created them.
Genesis 1:26-27
Finally, all three Persons are associated together on an equal basis in numerous passages:
Regarding Jesus' baptism
—Matthew 3:13-17 (voice of the Father, Son baptized, Spirit descending like a dove).
Regarding Salvation
—1 Peter 1:2 (chosen by the Father, sanctified by the Spirit, sprinkled with the blood of Jesus).
Regarding Sanctification
—2 Corinthians 13:14 (grace of the Lord Jesus, love of God, fellowship of the Holy Spirit).
Regarding Christian Baptism
—Matthew 28:19 (baptized in one name, yet three Persons—Father, Son, and Holy Spirit).
Regarding Prayer
—Ephesians 3:14-21 (strengthened by his Spirit, know the love of Christ, filled with the fullness of God).
Regarding Christian Growth
—2 Thessalonians 2:13 (chosen by God, loved by the Lord, sanctified by the Spirit).
Now the way that I have come to understand that correlation as in a family ...
I, my father, mother, brothers, sisters, ... and some uncles, aunts, cousins, etc. all SHARE the same last name (let's say "Harris") ... and could be referred to, correctly, by that name ... at any given time. In fact, that was the sole way that my mother-in-law would refer to me .... "Harris ... ".
So, we are ALL correctly identified as "Harris", ... though, at the same time, we are all DIFFERENT persons. We are ALL "Harris".
In the same way, I believe that God is a family (which christians call the Godhead/Trinity), made up of the Father, the Son (Jesus), and the Holy Spirit.
This is not surprising, ... since God is a God of families.
The concept really is not all that difficult ...