The advertising suggests that the new 6W bulb generates as much light as a 40W incandescent light used to. Most of the energy in an incandescent light bulb is converted into infrared radiation that we can't see or it's at the red end of the spectrum where the human eye is not very sensitive. This
is a typical incandescent spectrum and you can see how little of the emissions fall into the visible. All the power outside of the narrow visible band is wasted.
In comparison, a modern LED lamp contains a blue emitter chip and a yellowish phosphor, the spectral contributions of both can be seen here:
Please note that the emissions in this graph only cover the visible waveband, which is not the entire physical truth, of course, the graph is just cutting out the emissions in the deep infrared due to the low temperature heat that the bulb is still emitting. Despite this omissions, the total conversion efficiency of electrical energy to visible light is still much higher than that of the incandescent light.
Having said all of that, some of the practical results with this kind of advertising will be disappointing. For one thing the industry has a bad habit of over-speccing their products (that is also the case for the incandescents!), for another, the radiation patterns of many of these lights are different and they may produce brighter light in one area but then fail to illuminate the entire room. I would expect to put, at least, 50% more "equivalent" lighting power in with the new lights than with incandescents to get similar results. That is still a significant energy savings. If you can trade 9W of LED lights for 40W of incandescents, that's savings of roughly 75%.