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.
Based on what you have written, your partner should not have redoubled with a "minimum supporting hand," which I take to be 6-9 points, perhaps more like 6-7 for reasons discussed below.

A redouble after an opening bid and takeout double means, "I think we've got them." It shows 10 high card points or more, which opposite your 14 means, "we've got at least 60% (out of 40) of the high card points between us.

You did the right thing to pass. If partner really had ten high card points, you would have made three diamonds. Two doubled overtricks are 200 points, and you would also have gotten 80 points below the line. If the opponents had fled to a major suit, you should have been able to double and set them with your partnership's presumed 24+ points, and relatively balanced hand.

The fact that you made only two diamonds, not three, suggests that partner had only 6-7 points; you and partner together had about 20, not 24+, and likewise the opponents, had about 20. (Unless this was an "unlucky" hand in which all the breaks and finesses went the wrong way.) If this was the case, one of your opponents should have bid one of a major, with the final likely contract being two of their major (which outranks two diamonds). 

Your actual result seems to have been "fortuitous," (although possibly wrong: partner probably overbid with a redouble and scared the opponents out of what should have been a plus score for them. Even if they went down one, their minus 50 not vulnerable or minus 100 vulnerable (neither doubled), would have been less than letting you have 280 at a redoubled contract.