In the given auction, West is the opener (everyone knows this one), North is the overcaller, East is the responder, and South is the advancer. (If there's ever a term used here that you haven't run across before, check out this site -- the Bridge World's Bridge Glossary.)
Now that we're speaking the same language, let's get to the convention. A nice competitive bidding device is Snapdragon. This is a double (we'll get to the redouble part later) by advancer. The only occasion when a double is Snapdragon is when three different suits have been shown by the other three players, and nobody has jumped. Something like this:
Here are two auctions in which a double is not Snapdragon:
In the first auction, there's been a jump bid; in the second auction, only two suits have been bid. In either case, Snapdragon is off.
So what does a Snapdragon double show?
Two things: Length in the fourth (unbid) suit, and tolerance (or better) in partner's suit. In my partnerships, we usually define "tolerance" as Tx or better. So, when I hold a hand like
T53 K6 AJT872 62
and the auction goes
(1C) 1H (1S)
to me, I double to show competitive (or better) values, length in diamonds, and honor-doubleton or better in hearts.
When I hold
T53 6 AJT872 K62
on the same auction, I bid 2D, showing values and length in diamonds but no tolerance for partner's suit.
Partner will be able to judge the later auction much better with the information about your length in his suit.
I've also been known to [ab]use Snapdragon with a hand like this:
T53 K876 AJT8 62
in the same auction -- (1C) 1H (1S), I'll Snapdragon double and then pop to three hearts, trying to show a diamond lead-directional raise to 3H.
What about the redouble? Well, let's look back at a very similar auction:
(1C) 1H (X)
The double shows [exactly four] spades, so why not treat the auction the same way as the previous one? Clubs, hearts, and spades have been shown, so redouble can logically be used as Snapdragon in this situation.