Resonance refers to a tendency of a system to oscillate more at certain frequencies than at others. Those frequencies are known as resonant frequencies.
An excellent example of acoustic resonance is shattering a wine glass with sound. Here's a quick explanation as to why the glass shatters:
The sound is being generated by a speaker. The speaker works by moving a small cone back and forth generating the appropriate frequency. You can sometimes see the movements.
Many frequencies make the glass vibrate, but only a handful make it vibrate so much that it cannot stay together. Those frequencies are the resonant frequencies—they make the glass vibrate (i.e. oscillate) much more than the other frequencies.
Since the glass is insufficiently elastic, it shatters.
What other resonant systems have you encountered?