Resonance is an operating condition where an excitation frequency is near a natural frequency of the machine structure. A natural frequency is a frequency at which a structure will vibrate if deflected and then let go. A typical structure will have many natural frequencies. When resonance occurs, the resulting vibration levels can be very high and can cause rapid damage.
In a machine that produces a broad spectrum of vibration energy, a resonance shows up in the vibration spectrum as a peak whose frequency is constant even as the machine speed is varied. The peak may be quite sharp, or may be broad; depending on the amount of effective damping the structure has at the frequency in question.