There are several reasons. The selfish one is because it's the only way to guarantee passage to Paradise. A Muslim can be devout, pray five times a day, make the pilgrimage to Mecca, etc., and still have to face judgment (with a chance of not making it to Paradise). But if he or she dies while killing non-Muslims, there is no judgment. The Muslim who dies in jihad goes straight to Paradise.
Another (less selfish) reason is that any Muslim who dies in jihad gets to intercede with Allah on behalf of seventy of his relatives. That's a big motivation for a would-be Muslim martyr. He will be able to help his mother, father, brothers, cousins, etc., get into Paradise. This also at least partly explains the assistance jihadis get from their less-courageous relatives.
The goal of orthodox Islam is to bring the whole world under the rule of the law of Allah, by peaceful means if possible, but by war if necessary. The Islamic system of law is so abhorrent to anyone not raised with it, it has become clear down through the centuries that war is necessary for the goal to be accomplished.
By blowing up non-Muslim civilians, the jihadi has created a double-bind. It is a no-lose situation for an orthodox Muslim — some non-Muslims were killed and that's a good thing, and if the jihadi dies doing it, that's fine too. If the non-Muslims don't do anything in response, it will encourage other Muslims to become jihadis because no consequences followed. If the non-Muslims make a strong response, at least some other Muslims will see this as "war against Islam" and will take up arms to join their brothers in the fight.
With all this in its favor, why not blow people up?