Alpha Testing and Beta testing is a commonly used Testing Technique. To Explain it :
1: Alpha Testing: Consider you have Gone to Electronics shop to purchase a TV. The SalesMan gives you a demo or walkthrough about the particular product that's Alpha Testing.
2: Beta Testing: The Same TV arrives at your Home and the concerned person starts demo of the product at your home that's Beta Testing.
Proper Definition you can get from website or any other place. But this is a basic thing for it...