DDS is short for direct draw surface. It has many advantages over TGA, most apparent of which are that it takes up a whole lot less video memory, and can automatically create mipmaps, which do wonders for FPS if used properly. It DOES NOT support bump mapping - bump maps don't work in real time, for that you have normal maps - and yes, dds format supports those as well.
Also, it's not exactly a new format, it's been around since directx7.