EDIT: Having read these great answers I feel a little ashamed for the fear I felt on this recent flight. However, judging by my reaction to the experience and the reaction of those around me on the flight I imagine I am not the only one who felt this way. As others have mentioned here I will agree that passengers are pretty bad at judging turbulence. For those who come to this Stack Exchange site with similar concerns, I hope that you read these answers from those knowledgeable in the field to assuage your concerns.
I was recently on a flight that flew in to central Texas coming from Denver. There was bad turbulence on the flight in the last 45 minutes -- the worst I have ever experienced -- and I was curious about what else was going on behind the scenes from the perspective of the pilot and crew.
I do not know the airplane model. It has ~38 rows and 3 seats on each side of the aisle. I was in row 35. It was a standard commercial airplane that would fly across the United States.
We were first told that we were about to enter a turbulent area based on reports of other airliners in the region. We soon entered an area of lightning and dense clouds so thick that there was no visibility outside the windows.
The first drop came unexpectedly in what I can only describe as similar to a bad, bumpy landing on the freeway. The bags rattled pretty hard and loudly and I felt myself leave the seat. It was loud and jarring enough for most of the people in my area to scream out loud. Over the next 45 minutes, these drops happened continuously and randomly, up to 15 times.
Between these big drops the plane felt like it was swaying from the left and right. There were also many tiny dips between the bigger dips. It was extremely tense for everyone on the plane and generally it felt very uneven below us so there was a constant anticipation of another drop.
After the landing gear went down, it was clear that we were ascending again. The pilot explained that there was a "spacing" issue on the ground so he was going to fly around and try to land again. The guy next to me said (jokingly?) that this meant the pilot was too scared to land.
The cabin crew looked pretty terrified, and they were chatting to each other throughout the whole ordeal. People were sobbing and weeping all around me and they would yell every time a drop happened.
Obviously, you have little information to go off of but I was curious, from what I have provided, about the following questions:
Many people on board were fairly traumatized by the experience. Was there any real danger from turbulence this bad? Is this something a pilot might encounter routinely that they would be equipped to handle or does this seem unusually bad?
What was happening behind the scenes? How does a pilot handle a situation like this? Was there other information about the turbulence that we were not being told?
Any other interesting, related information to give me insight into this experience would be appreciated.