How does vibration like from speakers produce sound?

Vibration is the action that produces pressure pulses through the air. These pressure pulses (within certain frequency ranges) are picked up by the ear converting them to sound. Speakers vibrate to produce such pressure pulses - the more accurate they are the better for sending clean pulses through the air. All speakers will have a certain frequency range they are best at producing. That is the reason there are woofers, tweaters, mid range, etc types of speaker - to cleanly produce pressure pulses within a certain frequency range the ear can hear.