Probiotic or lactic acid bacteria are responsible for turning milk into yogurt. Whether they simply pass through the gut or stick around and colonize, they're beneficial to the colon because they help maintain a favorable balance between beneficial and harmful bacteria. For probiotic bacteria in yogurt to be beneficial they must be alive.
How do you know the lactic acid bacteria are alive? Read the label on the yogurt container. It should say "active cultures" or "live bacterial cultures" or something similar. If the label doesn't say that, I'd assume they were dead. Some yogurt brands are re-pasteurized after being cultured, killing the probiotic bacteria.