Inside the Hyatt was an atrium area with two "skywalks" that were over 100 feet long that overlooked the dance floor.  The skywalks were fully occupied with spectators, watching the dance below.

At 7:05 pm, a loud cracking noise filled the room, and within seconds the walkways plummeted down, killing 114 people, and injuring over two hundred others.

This wasn't the first collapse that had occurred at the Hyatt.  Two years before the completion of its construction, the atrium roof had collapsed.  Improper expansion joints and structural connections were blamed for the collapse.  After the investigation was completed, construction continued with the suspension of the skywalks.  Then, just a year after construction was complete, the skywalks collapsed.

The explanation of why the collapse happened is really very simple, but a bit technical, so bear with me.  I'll give you a practical example after the technical stuff so that it will be easy to understand.

The original design called for a row of six steel rods to be suspended from the atrium ceiling structure that would support the entire length of the walkways.  The bottom thirty feet of the rods were to be threaded to accept washers and nuts.  The upper walkway would be constructed on the floor, then lifted up to its final height with the rods slipping through holes in its support structure.  Nuts and washers would then be spun up to the bottom of the structure.  Once the nuts were in place, then the temporary supports for the walkway could be removed, and the lower walkway would be installed the same way. 

Conceptually, the design worked, but in reality, it proved to be somewhat difficult and expensive to do.  No one wanted to twist a threading die over a thirty feet length on the steel rods.

The fabricators saw a way to avoid threading the rods.  They suggested that they suspend the rods down only far enough to support the upper walkway.  That way they would only have to thread the bottom six inches of the rod.  To support the lower walkway, they suggested that they suspend the steel rods from the upper walkway.  This would only require threading the rod for six inches at the top and six inches at the bottom.

What the fabricator did not realize was that instead of the load of the lower walkway being transmitted through the rod to the roof structure, its load was being placed on the upper walkway.

Think of it this way.  Two men are hanging from a rope.  One is hanging onto the end of the rope, and the other is halfway up the rope, barely hanging on for dear life.  The guy on the bottom climbs up the rope and grabs hold of the man above him.  Now the top guy is not only holding his own weight, but also the weight of the other man.  He isn't strong enough to hold the added weight, loses his grip, and falls.  This is exactly what happened at the Hyatt Regency.
There were other factors that contributed to the collapse, aside from the design change.

First, the earlier collapse of the atrium should have been a big clue that there was something systemically wrong with the design and construction team. 

Second, investigators found that the original design of the walkways was grossly under-designed to begin with, so the design change aggravated that condition right away.

Third, the shop drawings (the drawings that are used to fabricate all the parts and pieces) were given to a junior engineer at the structural engineer's office to check.  He saw that the rods and beams were the same size that his office had specified, but did not notice the difference in the design.

After the collapse, two structural engineers had their licenses permanently revoked for gross negligence and unprofessional conduct.  As you would expect, lawsuits against everyone involved, including the building owner, went on for years, resulting in millions of dollars.  The reports were that everyone's insurance was "limited out".

The tragedy of this collapse, besides the loss of life and injuries, was that a series of easily-recognized mistakes had been made by a series of people who were either incompetent or lazy, or both.  Thankfully, this doesn't happen very often.