Dynamic vibration behavior is the response of a structure under external excitation. Every object has its own series of natural frequencies. Once an external excitation matches the natural frequency of an object, resonance will occur. One common example you may be familiar with is plucking a guitar string. However, resonance can also have undesirable consequences such as increased vibration.
The question then becomes, how can we find the natural frequencies of an object so we can create or avoid resonance? In solid mechanics, we want to avoid resonance to protect the structure 99% of the time. Modal analysis is the answer here. We call modal analysis "free" vibration analysis.