JDM stands for Japanese Domestic Market. That is things that are made for and sold in the Japanese market. It particularly applies to things that can be had in Japan but are not officially sold in the United States.
You often see the term applied to engines, because Japan gets some engines in some cars that, while they can legally be used in the US, were never sold here; AND due to Japanese car registration laws, it can be expensive to keep older cars running, and therefore many are sold overseas, or parted out both in Japan and overseas, even though they don't have many miles on them. Thus you can buy a low-mileage JDM engine for not a lot of money.
Sometimes things are sold as JDM as a cover for selling stolen parts. This is a problem with Hondas/Acuras. It can be hard to prove whether parts are stolen (this is VERY common with GSRs and Type-Rs), and the JDM angle is believable, so...
JDM stuff carries a lot of cachet when you're talking about Japanese cars. Why? Because it does. Like European stuff does for VWs and BMWs, and I imagine American parts do for American cars overseas.
And you're going to look like an idiot driving a car with an outlandish body kit.