When something close to the
natural frequency of an object strikes it, you get an
amplification of its vibration. The easiest way to think of resonance is pushing someone on a
swing. You push them at
exactly the same frequency at the swing is swinging -- the swing's
natural frequency. Net effect: the person goes higher and higher. if you were pushing them slightly slower or slightly faster than the swing's frequency, you'd be out of sync, and the person wouldn't go as high.
You get the same phenomenon with sound, too. If you hum a perfect E, then you can actually see the string on a guitar start to vibrate at the same frequency. This is because it is resonating with your voice.
You can use resonance to do lots of curiously destructive things. For example, you know that stunt where the woman sings a note and the wineglass shatters? You can actually do it, and it is caused by resonance. The wineglass' natural frequency is the same as the opera singer's voice (you can work out the natural frequency by tapping the glass) and the vibrations caused by an opera singer's voice are violent enough to break the glass. There was a bridge made, called the Tacoma Narrows Bridge, whose natural frequency just happened to match the winds that used to strike it. This eventually caused the bridge to collapse, barely three months after it was completed. Finally, using infrasound, you can actually cause a person's organs to rupture and kill them if you cause them to vibrate at their natural frequency which is 3 to 7 Hz. This has happened.