It may help if we break down the sentence into two parts.
"The time is right" means this is the right time to take action, or it is the right time for something to happen. "The time is always right" means that the right time to take action is all the time.
"To do what is right" means to take actions that society defines as good.
Combined, the phrase means you should be doing good deeds all the time, that there is not any reason or excuse to push it off to do later.