These edits adopt the prequels' assumption that the audience is already familiar with what came before. As such, the best answer is Old Ben's exposition that, "to protect [them] both from the Emperor, [they] were hidden from [their] father when [they] were born."

Within Episode III, it's partially addressed (or, more accurately, sidestepped) in the scene between Obi-Wan, Bail, and Yoda aboard the Taintive IV whatever-the-hell. My version hopefully telegraphs to the unsuspecting audience that a conversation is just coming to an end. It reads:

"Hidden, safe, the children must be kept. Until the time is right, disappear we will... Master Kenobi, wait a moment..."

The scene doesn't end there, but that's how it opens.