The concept of the Trinity is fundamental to Christianity, yet it's also the most difficult to understand. Christians believe there is one, and only one, God. God exists as three Persons: the Father, the Son (Jesus Christ), and the Holy Spirit. Each Person is fully and simultaneously God: they all have the same attributes (omniscience, omnipotence, etc.) and the same essence, or nature. Because they have the same essence/nature, they have the same knowledge, the same reactions, the same desires: they are the same being, God.

To me, the simplest explanation is found in the Bible in John 1:1: "In the beginning was the Word, and the Word was with God, and the Word was God." ("The Word" is another name for Jesus.)

For more information, see Is the Trinity Biblical?