A beta test is a limited release of a product with a goal of finding bugs before the final release. Software testing is often referred to by the terms "alpha" and "beta."
Generally speaking, the alpha test is an internal test to find bugs, and the beta test is an external test. During the alpha phase, the product is opened up to employees of the company and, sometimes, friends and family. During the beta phase, the product is opened up to a limited number of customers.
Sometimes, beta tests are referred to as "open" or "closed". A closed beta test has a limited number of spots open for testing, while an open beta has either an unlimited number of spots (i.e. anyone who wants to can participate) or a very large number of spots in cases where opening it up to everyone is impractical.