Well Graham,
I've never had to use a transformer cable since the 80s, but apparently, Korg has designed a mic input that really is quite fussy about impedance.
Here's the simplest way I can describe why you need it:
All mics are either hi or low impedance (That's the resistance that the mic creates in the energy path to the amp), so a low impedance mic will present a very small level of resistance to the input, and a high impedance mic will produce quite a bit more. Makes sense, right?

In the past, I've used a cable that had an XLR at the mic end and a 1/4 at the amp end and it simply connected the pins from the mic to the tip and sleeve of the jack. That used to be enough, but in a more particular setting, like this new Korg ... the built in mic input EXPECTS a high gain signal, and if you don't use a transformer (or transformer cable) the impedance will be mismatched. Like the round peg/square hole analogy.

A simple in-line transformer will raise the impedance of a low-z mic to match the impedance of the Korg input, so there is no signal loss. Signal loos translates into less than beautiful tone and clarity. You can get transformers all over, but they are about 3-4 inceh long and will stick out of your keyboard, just BEGGING to be bumped into and broken, so I recommend a cable with the transformer built right in, IF you're using a Lo-z mic, like a Shure SM57,58 or the EV 767, 757, 747 etc. There are high z mics out there (Radio Shack, Best Buy), but the sound quality is not up to what you're probably used to, so I think the cable is a better solution.
Check this out and call one of our dealer friends:

http://www.rapcohorizon.com/p-62-transformer-microphone-cable.aspx

Good luck!