What is meant by degrees of freedom of a molecule?

Answer 1

Degrees of freedom is a concept taken from mechanical engineering. I like to visualize those articulated factory robots. They rate these robots based their number of axis or degrees of freedom. They call the end of arm turny-bit one degree, the wrist a second degree, the elbow a third degree and so forth.

http://en.wikipedia.org/wiki/Factory_robot

A molecule can be seen in much the same way. For each additional bond, you gain additional modes (ways) of movement.

So with a binary molecule (one bond) the only mode you have is stretching (vibration)
With a tertiary molecule (two bonds) you have stretching and bending (wagging).
With a quaternary molecule (three bonds) you have stretching, bending, rotation

Is this starting to look familiar? Along the axis of each bond, stuff can happen to contort that molecule. A molecule with 10 atoms can contort itself much more than a molecule with 5 atoms. Each bond (axis) is a degree of freedom for movement.