Consider six people standing in a line.

They can be arranged in

distinct ways.

Now suppose we arrange these people around a circle. The following permutation are not unique.

As one can become the other form rotating the table.

To solve this problem to keep one person fixed and arrange the other around the fixed person. so there will be

unique arrangements.

I hope this clarifies where the

comes from.

Side note:

In particular cases you will not consider clockwise and anticlockwise wise circular arrangements as being unique. For example, consider arranging beads in a necklace clockwise and anticlockwise arrangements are not consider unique and you can "flip" the necklace around to go form one to another. So in particular cases you may need to use

Bobak