the [Black] (in square parentheses) is the default black and cannot be deleted from the palette. it is also special in that by default (unless turned off in the preferences), 100% of this colour within indesign will overprint. that is, any type, strokes or fills set in indesign to 100% [Black] will overprint unless told not to in indesign's preferences.
the other black made as a new process colour is, well, black, but will NOT overprint by default. this colour CAN overprint if told to in the attributes palette.
within PROCESS artwork, the default [Black] is generally good for type under 60pt, strokes, and solid blacks which occupy a small space and are NOT above any kind of image.
the black made as a new colour is good when the black has to knock out of the colours underneath. a good example white text reversed out of a black box above a photo. if the default black is used, the photo beneath will be visible and any misregistration on press will be more observable. if the new colour black is used, it will knock out of the picture below.
maybe this will help: http://wp.me/p1x3Yg-W
In your Prefernces>Appearance of Black is the "Overprint [Black] swatch at 100%" ticked?
It's noteworthy too that in regards to overprinting the black swatch InDesign has two different behaviors with Black @ 100%. If you use [Black] it will fall under the Document Setting for overprinting (always overprint Black Swatch @ 100%) and if you use 0-0-0-100 it will always knock the black out unless overprinting is chosen at an object level or via a multiply attribute.