It's a plethora of reasons.

First: The people at the back want to see what's on the front, so they push forward. The pushed people unintentionally push the people in front of them, and before you know it, you have a whole crowd that turns into human liquid. The more in front you are, the worst is going to be. Imagine it like a wave where the bit that touches the shore is the first one to curl and break, and the rest crashes on top.

Second: The people at the front are trying to back up from what's on the front, so they push the people behind them with their backs. This type of crowd surge is usually the easiest to trip in and fall backwards. If you fall, the chances for survival are very slim. Anything from asphyxia to broken bones piercing your organs can easily kill you.

Third: There are lots of assholes, or people that think they know better. If you start pushing forward, and the people in front yell at you to stop, STOP! Listen to them. It's not funny, the crowd isn't there just for you, you wouldn't like someone to do that to you, and if you keep pushing, you will be complicit in killing people. Granted, you're not pushing in order to kill them on purpose, but your actions will certainly end the lives of many others.

Fourth: People are so tightly cramped that their lungs become unable to expand properly, which usually leads to shallow breaths that inevitably result in people getting passing out, or getting completely asphyxiated. If your four corners are touching someone else, you're already in danger. Always make sure to have at least one corner free of people.

Fifth: People trying to go against the push of the wave. If there's a wave, the best thng you could do is allow it to take you, and DO NOT FIGHT IT. A lot of people in their justified desperation try to turn around, and fight the massive horde of liquid people coming at them with full force. You're not going to win against thousands of pounds pushing against you. Think of it like a Tsunami, and someone trying to stop the insane amount of pressure coming at them. People will accidentally knock you down, knock you out, or get you cramped against somebody, or someone else.

Sixth: Lack of crowd control from the event organizers. This is laziness and negligence on their part. A lot of disasters could be avoided if the guys in charge controlled the flow of people, and prepared for bigger crowds.

Seventh: Pray to whoever you pray to that there isn't a wall at the end of the wave. The wall is ALWAYS going to win. People are getting absolutely crushed, and the wall won't budge. Broken bones piercing organs, asphyxiation, and getting knocked out are the most common ways to go here.

Here's a great comment from years ago explaining in great detail how it happens. Please give it a read if you want know more, but be forewarned that it might be a little too intense for some.