Why is ISIS taking hostages, beheading them, and broadcasting their deaths on the internet?
I'm not asking "Why" as in "Who would be so evil to do this?", but as in what are their stated and/or actual goals in doing this.
You might find this article useful. It lists some of the reasons.
There's a lot it doesn't say, though, so I'll try to cover this adequately. First, understand a couple of things. Islamic State is not a political force as much as it is a military/religious one. This means that they might do stupid things (and many agree that beheading these people as a tactic to deal with the west is one of these). Second, understand that you probably won't understand their actions because they are not rational. These people are as fanatical as they come, so much so that Bin Laden believed them to be too extreme. "You were excommunicated… by a gang… of psychopaths!" And they don't talk to western journalists, either, which makes it difficult to get their point of view. With that in mind, here are a few reasons why they're beheading any westerners they can get their hands on.
Terrorism as an offensive weapon. The reason they were able to take over Iraq so easily was because the Iraqi army ran away from them. Their terrorism tactics work in the middle east, because the people that would oppose them are generally moderates whose beliefs just aren't as extreme as theirs, people getting paid not nearly enough.
Terrorism as propaganda. They want to show to world they're hitting back against the west in response to western physical attacks, but the only way they can do that is to behead hostages. Extremism is a good thing to Islamists, they want to see it, and given that western governments are now hitting them, this is their next step. Here's a key point: this does work. Many Islamists are flocking to them because a caliphate is something they've have wanted for a very long time. They want to rally behind a group that fulfills their ambition of a world ruled by Islam. IS also need to keep their own people together and to keep their momentum up. They need to be seen to be doing something to fight back.
Demonstrating that they're doing what they promised. They're trying to carve out a caliphate, which means they have to enforce strict sharia. To them, these people are guilty of the unpardonable crime of not being Muslim. They're trying to prove that they're not just fighting back, but carrying out rulings of law. To us they're committing crimes against humanity, but to them, they're living the dream.
Their stated aim of dissuading us from attacking them. They view western nations as weak-willed and if they can, they want to persuade us to withdraw. Their view of morality is based entirely on scripture and the people they admire, so it's probably difficult to understand why we'd care about the lives of people that we are unaffiliated with, so they attack us where it hurts.
I would love to get information straight from the horse's mouth on this one, but we have to rely on observations and facts as viewed from outside. My understanding could be way off (it must be, I suppose, for me to view it as evil). I'm afraid I'm obviously biased, but then the arguments by one of them would likely be incomprehensible to us.
From my point of view regarding what IS did to the Jordanian pilot (especially if it's true that they burned him a month ago), I believe IS is sending a message to the public opinion in the western countries. This message urges peoples not to invest in war against IS and frightens every soldier who may be in Jordanian pilot's shoes, ending up abandoned by his government. The fact that IS trying to deliver this message can be proved by consider the well prepared video series "Lend Me Your Ears" in which the British captive John Cantlie present himself every time as the citizen who was abandoned by his government. It worth mentioning that IS benefited from the coalition air strikes by marketing itself for all jihadists around the world as the Islamic state that is fighting the evil of the west in general and US in specific, this marketing propaganda attracted many jihadist around the world to join IS. However, the idea of the west investing in ground attack against IS is not in IS's interest. From what I see, I think that IS with all the professionalism that cannot be denied in producing and marketing their media is sending messages should not be read superficially.
Also, ISIS is sending a marketing advertisement to its followers around the world.
Easiest answer to this question would be that it is a high source of income, money. Apparently most of the income terrorist organizations get come from ransom in kidnapping cases.
Although governments condone negotiations with terrorists and is in fact illegal in some countries, there have been cases where they pay through multiple foreign cover charity and humanitarian organisations/ministries to bring their citizens back into safety.
This information however comes from a local documentary that was broadcasted on national television recently and thus I have no additional sources at the current moment to back it up. Be free to take it with a grain of salt and correct me.