I think the nicene creed is as good an explanation on the trinity as you can get really:
‘I believe in one God,
the Father almighty,
maker of heaven and earth,
of all things visible and invisible.
I believe in one Lord Jesus Christ,
the Only Begotten Son of God,
born of the Father before all ages.
God from God, Light from Light,
true God from true God,
begotten, not made, consubstantial with the Father;
through him all things were made.
For us men and for our salvation
he came down from heaven,
and by the Holy Spirit was incarnate of the Virgin Mary,
and became man.
For our sake he was crucified under Pontius Pilate,
he suffered death and was buried,
and rose again on the third day
in accordance with the Scriptures.
He ascended into heaven
and is seated at the right hand of the Father.
He will come again in glory
to judge the living and the dead
and his kingdom will have no end.
I believe in the Holy Spirit, the Lord, the giver of life,
who proceeds from the Father [and the Son],
who with the Father and the Son is adored and glorified,
who has spoken through the prophets.
I believe in one, holy, catholic and apostolic Church.
I confess one Baptism for the forgiveness of sins
and I look forward to the resurrection of the dead
and the life of the world to come. Amen’
I once read someone describing it by saying you should imagine a woman who is a mother, friend, and doctor.
The version of her that carries out each role is different. She wouldn’t rock her patients to sleep or turn to her children about issues in the bedroom… but she is still the same individual whether she is diagnosing patients at work, on a night out with friends, or tucking her children in at night.