Panic attacks are sudden periods of very bad anxiety. Along with feeling very scared, people with panic attacks usually have physical symptoms.  These symptoms are not dangerous.  However, they can make a person feel terrible for a short time.  Having a panic attack is often terrifying and very upsetting.  Many people who have a panic attack for the first time call the emergency services because they think they are having a heart attack or a nervous breakdown.

Though panic attacks make people feel terrible, they are not dangerous. Usually, the worst symptoms are over in ten minutes or less. However, some panic attacks can be as short as one to five minutes.

Panic attacks can happen in people with all kinds of mental illnesses.  They can also happen in people who do not have mental illness, but have just had something very bad happen to them. 

A panic attack is sometimes confused with anxiety. Anxiety is progressive, when we think of negative thoughts, the anxiety becomes worse when we do not try to relax and it reaches to a point when we're out of control. A panic attack is not progressive, when we think of negative thoughts, a panic attack goes straight to us feeling out of control and people would often think they're having a heart attack because an anxious heart feels very similar to a heart attack. A panic attack is far worse than an anxiety attack, though both attacks require the person to learn how to calm down or get professional help if it becomes a problem in their daily lives.

Symptoms 
The new Diagnostic and Statistical Manual (DSM), DSM-5, describes a panic attack as:

"An abrupt [sudden] surge of intense [very strong] fear or intense discomfort that reaches a peak within minutes...  [During that] time four or more of the following symptoms occur. The abrupt surge can occur from a calm state or an anxious state."

According to DSM-5, a person is having a panic attack if they suddenly start feeling very scared and have four or more of these symptoms:
 Palpitations (a pounding heart) or fast heart rate
 Sweating
 Trembling or shaking
 Feeling unable to breathe
 Feeling of choking
 Chest pain or discomfort
 Nausea or other gastrointestinal problems
 Feeling dizzy, unsteady, lightheaded, or faint
 Feeling hot, or feeling chills
 Paresthesias (numbness or tingling feelings)
 Derealization (feelings of not being real) or depersonalization (feeling detached from oneself)
 Fear of losing control or going crazy
 Fear of dying

The physiology behind panic attacks 
Panic attacks happen when the body's natural fight or flight response gets overprotective.  Usually, the fight or flight response kicks in when a person is in danger.  It tells the sympathetic nervous system to make many changes in the body.  These changes will help the person fight or run away from the danger.  For example:
 The person will get scared.  This makes them want to get away from the danger they are in.
 The heart will beat stronger and faster.  This will get as much blood and oxygen to the body as possible.
 Chemical messengers like epinephrine (adrenaline) will be sent out through the body, to give the body extra energy to fight or run away.
 The body will stop digestion in the digestive tract.  The body does this because it wants to spend all its energy on fighting or running away.  It does not want to waste energy on things like digestion which will not help the person escape danger.
When a person is truly in danger, these changes in the body can help the person survive.  The changes in the body make it easier for the person to fight or run away from the danger.

However, when a person is having a panic attack, their body is reacting as if they are in danger, when they are really not.  Their fight or flight system kicks in and causes changes to the body.  But because the person does not need these changes to help them survive, the changes cause symptoms.  For example:
 The person will feel very scared, even though they are not actually in danger.
 The person may notice that their heart is pounding (because it is beating stronger) or beating quickly.
 The person may notice side effects from the epinephrine that is being sent out through their body.  Those side effects can include sweating, chest pain, and feeling even more anxious.
 Because digestion has suddenly stopped, the person may have nausea, diarrhea, or other gastrointestinal problems.

Every symptom of a panic attack is caused by the fight or flight reaction.  This is why panic attacks are not dangerous.  The fight or flight system is meant to save a person's life if they are in danger.  It is a natural self-defense system in the human body.  When a panic attack happens, this life-saving fight or flight system is simply kicking in when it is not needed.

Related pages 
 Panic disorder
 Anxiety disorder
 Pan (mythology)

References

Other websites 
What Is Panic Disorder?  What are Panic Attacks?  from AnxietyBC.com (Simple English)
Panic Attacks: The Hallmark of Panic Disorder by the American Psychological Association 
Panic disorder from PubMed Health

Anxiety disorders