Jesus and his cousin (Matthew 3; Mark 1; Luke 3; and John 1)

John the Baptist lived in the desert countryside until one day the Spirit of God landed on him.  He then started going around the countryside baptizing people and calling them to repent.  This garners a lot of attention and throngs of people come to him.  Combining the accounts, we know of at least 4 groups that came to him - Pharisees, Sadducees, soldiers, tax collectors.  Each group asked what they should do and his answer was specific advice about treating other people better.

The fame and influence of John the Baptist grew so much that people even asked him whether he was the Messiah, the "Prophet", or even Elijah.  Clearly, his respect was high and he fit people's expectation of what the Messiah or Elijah would be.  Elijah is an interesting choice and may have been specified because Elijah did not "die", but rather was taken up to Heaven by an angelic chariot.  The question indicates that the people speculated that Elijah may have returned from Heaven.

When Jesus is about 30, he goes to John for go be baptized.  Jesus and John were cousins (first, second, or greater, we don't know).  So, we can probably infer that they knew each other from family events.  John may have even been in the company with Jesus' family when Jesus stayed behind the temple as a twelve year old.

John tries to get Jesus to baptize him, but Jesus persists that John must baptize Jesus.  John does this and as Jesus is coming out of the water, the Heavens open up and the Spirit of God descends on Jesus like a dove.  Then a voice says, "this is my son, in whom I am well pleased."

All four Gospels have this story, albeit with a slightly different focus of details.  The fact that all four Gospels have this highlights the significance of it.  Of course, it was important for Jesus to be baptized.  But I think the importance of the story is the connection between the ministry of Jesus and the role of John the Baptist as the messenger to pave the way for Jesus.  

The whole community loves John.  He is precisely what they expect in a prophet or even a Messiah.  His credibility is established.  

However, John repeatedly states that his role was a messenger to prepare the way for someone greater.  Here, we see the beginning of the transfer of importance from one person to another.  It is time for Jesus to rise and John to begin stepping down.