In the New Testament, Son of Man is a term that Jesus used to refer to himself. There is some debate about what exactly the term means. There are three basic interpretations within Christianity.
First, there is the idea that it is a designation for the Messiah. This interpretation states that Jesus believed that he was the Messiah of Judaism. He was aware of the apparent Messianic figure from chapter seven of the Book of Daniel whose appearnce was like "a Son of Man". In this interpretation, Jesus used this phrase as a display of his self-conciousness as the Messiah.
The second interpretation states that Son of Man is a generic term of self-reference. This interpretation concludes that Son of Man was a term of self-reference equivalent to the use of "this man" in contemporary English. One difficulty with this interpretation is that there are no known references other than the gospels in which a person uses the term Son of Man. Only Jesus uses this term in the gospels.
A final interpretation states that the meaning of Son of Man has been lost throughout the course of time. Nobody actually knows what the term means in contemporary times.
As an aside, some scholars believe that Jesus never actually used the term. Instead, these scholars believe that it was acribed to him later by the early church. According to this belief, the early church desired to demonstrate a self-reference by Jesus as the Messiah, and falsely ascribed them to him.