Question
What is the Trinity? (one God in three persons, and where the Bible teaches it)
Analysis
Held together from the whole Bible
No single verse states the doctrine in one sentence; it is the only way to hold all the Bible's data together. Scripture insists relentlessly that God is one (Deuteronomy 6:4; Isaiah 44:6), so Christians are monotheists, not believers in three gods. Yet it also calls the Father God, presents the Son as God ('the Word was God,' John 1:1; Thomas calls the risen Jesus 'my Lord and my God,' John 20:28), and treats the Holy Spirit as God (lying to the Spirit is lying to God, Acts 5:3; Acts 5:4). And the three are clearly distinct, the Son prays to the Father and sends the Spirit (John 14:16; John 14:26), and at Jesus' baptism all three appear at once: the Son in the water, the Spirit descending, the Father's voice from heaven (Matthew 3:16; Matthew 3:17).
What it does and doesn't mean
The doctrine deliberately guards against two errors: it is not three separate gods (that denies Deuteronomy 6:4), and it is not one person appearing in three modes or masks (that denies the distinctness seen at the baptism and in Jesus praying to the Father). Jesus can say 'I and the Father are one' (John 10:30) while also being distinct from the Father. The blessing of 2 Corinthians 13:14 names all three together, grace from the Son, love from the Father, fellowship of the Spirit. The 'how' remains a genuine mystery that no earthly analogy fully captures; the Bible asks us to affirm what it teaches, not to fully explain it.
A note on those who reject it
The Trinity is affirmed by the vast majority of Christians across Catholic, Orthodox, and Protestant traditions, formalized in the early creeds (Nicaea, AD 325). Some groups reject it and read the same verses differently, the deity of Christ specifically is treated in the "Is Jesus God?" answer, which lays out the mainstream and non-Trinitarian positions side by side.