The formula used in the GIMP is Y = 0.3R + 0.59G + 0.11B; this result is known as luminance.

This formula is not only used in The Gimp, but also in television. In order to make the color signal grokkable by B&W TV sets, a backward compatible signal is used, consisting of this liminance as the main signal, which means it is what you get to see on B&W sets; plus two extra color difference signals modulated on top of that.

From what I gather, both NTSC (USA) and PAL (Europe) use the same mechanism.

Common abbreviations in literature are YUV and YCrCb — "Y" is the lumninance signal, U and V resp. Cr/CB are the two other, "chroma", signals . Look here for an intro, for example.