Basically, the Neon Markers are artistic markers with fluorescent inks. The construction will be very familiar to anyone who has used ProMarkers from Letraset. Only discernible difference is that ProMarkers have small bullet tip on one end and larger chisel tip on the other, whereas Neon Markers have a bullet tip on both ends, one small and other larger.
The idea of fluorescent colours is that the colour appears impossibly bright, as if it was reflecting more light than there is. In fact, the colour is taking in light of a high frequency, such as ultraviolet light, and emitting it on lower frequency, such as yellow light.
The fact that Neon Marker colours react to ultraviolet light makes them especially attractive to situations where there's plenty of such light present. These colours will literally shine in places illuminated with little ordinary light and several blacklight bulbs.
Many of you may have already noticed that this fluorescent property is nothing new: in fact the common highlighter pens contain similar ink. I tried some highlighter pens I have and compared them to these Neon Markers. The colours hues are really similar to each other, but the colours of Neon Markers are clearly more saturated and vibrant than the colours of highlighters.
Here are the Neon Marker colours with some similar colours from the ProMarker range.
Here are the same colours when illuminated with a small ultraviolet torch.
So, to recap: these markers are so-so when the result is reproduced on computer screen. They are a lot better when people can see the original drawing you made. And when the original drawing is displayed under ultraviolet light aka. blacklight, that's when these markers work the best.