A body disturbed from its rest position tends to vibrate at certain frequencies called natural, or resonant frequencies. For each natural frequency, the body takes a certain shape called mode shape. Frequency analysis calculates the natural frequencies and the associated mode shapes.
In theory, a body has an infinite number of modes. In FEA, there are theoretically as many modes as degrees of freedom (DOFs). In most cases, only a few modes are considered.
Resonance is the excessive response that occurs when a body is subjected to a dynamic load vibrating at one of its natural frequencies. For example, a car with an out-of-balance tire shakes violently at a certain speed due to resonance. The shaking decreases or disappears at other speeds. Another example is that a strong sound, like the voice of an opera singer, can cause a glass to break.
Frequency analysis can help you avoid resonance by calculating the resonant frequencies. It also provides information to solve dynamic response problems.