TDI = new turbo charged diesels with fancy fuel injection. The only models available in the US are from VW, and I believe they aren't selling really well. But, they're becoming very popular in Europe.
The good side? Better fuel economy than gas, with very low emissions and decent performance -- or so they say (I haven't driven one). The bad side? I believe they require a better grade of diesel (low sulfur?).
Oh, and I've also heard that lower taxes on diesel (compared to gas) are another motivation in Europe.
Since I'm not a TDI expert, any corrections or additions welcome.
Tony