Question: Here is the situation. Playing best of minors (with four diamonds and 14 points with no five card suit) I opened one diamond. Opponent on my left Doubled. My partner Redoubled. Her partner passed and I passed…not comprehending what she was telling me or asking. As it turned out she just thought it was the right thing to do having four diamonds and a minimal supporting hand. We made two diamonds, and scored it accordingly, but left all of us still wondering what the Redoubled meant. 

What could it have meant, or what should it have meant under the Goren system of bidding? Was redoubling the right thing for partner to do with a minimum supporitng hand?

Answer: 
Playing a basic Goren system the Redouble (of a Take-Out Double of an opening 1 of a suit bid) shows a hand of 10+ points. It tends to show a balanced hand as it suggests that Opener Double the escape by 4th hand if it is into a good 5-card suit (or 4-card suit at the two level) in his hand, otherwise pass. It also tends to deny good support in Opener's suit for the same reason, as with a good fit Opener's side may find more profit in a Game contract than in penalizing the opponents.

The more strength there is in Redoubler's hand the more likely that it is short in Opener's suit, again because the likely profit in a penalty double increases from the potential mis-fit.

With sound support for Opener's suit the modern tendency is to make a pre-emptive raise: to the 2-level with 4-6 HCP and good 3-card support and the three level with 7-9 HCP and either a side-singleton or 4-card support and a doubleton. 

For the situation you described Fourth hand should have taken out the redouble: You scored a nice profit considering the opponents can probably make 8 or 9 tricks in a major themselves.
The redouble is not forcing on the original bidder, so the responder must be willing to see the hand played in the bid contract. That means:

1. The responder has support for the original bid (at least 3 diamonds, and at least six points.)
2. The responder must have neither the points or the distribution that would make game (or a slam) virtually certain -- otherwise bid a new suit or NT.
3. The responder does not have a hand thaat would make a preemptive raise reasonable, to prevent the opponents for finding game or slam.