He was an itinerant preacher, who spoke about the coming kingdom of God, urging his fellow Jews to get their lives in order so when the day of judgement arrived they would be judged righteous, not sinful (eg Mark 8:34-38). Among other things, Jesus urged his followers to give up all worldly goods (Mark 10:17-31), which is exactly what he did himself. We get hints that he was knowledgeable of Jewish law, but that his family thought him crazy (Mark 3:21), and people in his home town were not impressed (Mark 6:1-6).
He healed the sick and drove out demons, but this was not as exceptional as we might think:
He did not claim to be God, or part of the trinity.
It is questionable whether he even claimed to be the Messiah, but it seems others hailed him as such anyway. Mark 12:35-7 suggests he was not a descendant of David, but claimed to be a messiah anyway:
Mark 12:35 And Jesus answered and said, while he taught in the temple, How say the scribes that Christ is the son of David?The text is not too clear, but to my reading, Jesus is saying the David (in Psalm 110) is talking to both God (The Lord, Yahweh in the Psalm) and the messiah (my Lord), and if David is calling the messiah "lord" then the messiah cannot be his descendant (the son is always less than the father; the father owns the son, the lord owns his subjects; how can the messiah both be owned by David and owen David himself?). It is sufficiently ambiguous, of course, that later genealogies would be invented to cover the issue.
36 For David himself said by the Holy Ghost, The Lord said to my Lord, Sit thou on my right hand, till I make thine enemies thy footstool.
37 David therefore himself calleth him Lord; and whence is he then his son? And the common people heard him gladly.
Mark 11:1-11 describes Jesus' arrival in Jerusalem. If this really happened as described (and my guess is it is an exaggerated account of a real event), then it is likely this was the reason for his crucifixion. The Romans knew the Jews were waiting for a prophesied Messiah to lead a revolt against Roman rule, and an entrance like this was proclaiming Jesus as that messiah. In Mark 15:9, we see Pilate calling Jesus "the king of the Jews"; it is doubtful it happened like that, but Pilate probably saw Jesus as a claimant to the title, and therefore someone who needed to be dealt with.
Crucifixion was the punishment for treason; it was not the punishment for blasphemy. The Romans had a very relaxed view of religion, and did not give a hoot about blasphemy. The Jews certainly did, and James was executed by the Jews for blasphemy (Antiquities of the Jews 20.197-203), but this was by stoning, as required by scripture (Leviticus 24:16).
Mark is very clear on why Jesus was crucified:
Mark 15:25 It was nine in the morning when they crucified him. 26 The written notice of the charge against him read: the king of the jews.Although Christianity has later distoirted the truth, Jesus was executed by the Romans for treason, as a rebel leader.
It was usual practice to leave the body on the cross, but this was offensive to the Jews, and in times of (relative) peace the Romans would allow the bodies to be buried to avoid unrest. That did not mean honourable burial, however, merely that the bod was in the ground. The Romans had good reason to refuse honourable burial - they did not want to create a martyr, a symbol for rebellion - and no reason to permit it.
Assuming Jesus' body was taken down from the cross, it is almost certain he was not buried in a tomb, but in a nearby communal grave for crucifixion victims.
This is discussed in more detail here.
Failed MessiahMost Jews rejected Jesus as a false messiah at his crucufixion.
A century later they rallied behind Simon Bar Kokhba, another man perceived to be he messiah. Bar Kokhba is important to this discussion because he shows us what the Jews expected and what thew Romans feared. He was a military leader, who successfully ejected the Romans from Israel, at least for a time, before the Romans pretty much wiped out the Jews in Judean.
As with Jesus, in the Jews later rejected Bar Kokhbar as a false messiah.
Death and rebirth... of the cultWhen Jesus was arrested, his disciples fled Jerusalem, and Mark alludes to this:
Mark 14:27 “You will all fall away,” Jesus told them, “for it is written:So do does the Gospel of Peter:
“‘I will strike the shepherd,
and the sheep will be scattered.’[d]
28 But after I have risen, I will go ahead of you into Galilee.”
 But we twelve disciples of the Lord were weeping and sorrowful; and each one, sorrowful because of what had come to pass, departed to his home.Jesus' cult was dead, his followers returned to their former lives.
But weeks, or even months, later something happened in Galilee, and Peter saw something he understood to be Jesus resurrected. Later the other disciples saw it too, and later still a huge crowd witnessed it. The cult was reborn.
Was it really Jesus? I guess not, but we have next to nothing about what was seen in Galilee, so who knows?