Christians believe that Jesus is both God and man. The Gospel of John describes how he existed as the eternal Word of God prior to creation, and then became flesh, dwelling among us. It is why he is spoken of as God the Son, the second person of the Trinity. To his critics, Jesus said:
Before Abraham was, I AM (John 8:58).
The grammar is as shocking in Greek as it is in English--but it is completely intentional. Jesus is claiming an identity with the one who revealed his name as "I AM" in the burning bush (Exodus 3:14). The letter to the Hebrews begins with a series of quotations from the Old Testament to describe the Son, including quotes from a Psalm that is addressed to YHWH (see Heb. 1:8,10-12; Ps. 102:25-27).
As for the humanity of Jesus, there is very little dispute over this. The second chapter of Hebrews, following on the heels of the confession of Jesus' divinity in chapter one, is an exposition of Jesus' humanity and identification with the people he came to save. The first chapter of Matthew, identifying Jesus as the heir of Abraham and David, further shows God's concern with real, historic humanity in sending the savior. Hence, Christians confess that Jesus possesses a complete divine nature and a complete human nature in one person.
Of course the humanity of Jesus includes as well his identity as the Messiah of Israel promised in texts as diverse as Isaiah 53, Psalm 2, Psalm 110, and others.
Jesus' work is also described in terms of the covenantal offices of prophet, priest, and king. As prophet, he delivers the word of God. As priest, he offers sacrifice on behalf of his people, and as a king he saves and defends his people.
These, however, shall be treated individually later.