A guy who cut the first film. He/she's a cutter of negatives, so "neg" is an adjective on the person/people.
Celluloid film, as in real "film", the original, used to be a process that produced a negative image on the first use.
For a black and white photo, this means that dark areas of the scene are light on the negative and light areas are dark. Light areas of the negative are clear. Dark areas are dark, not letting light through.
The next process was to print this film onto paper which was the photo that you would get to look at. This process shone a light throught the neagtive, so any areas of the negative that were clear let light through and exposed the photgraphic paper, which reacted by turning dark. This making it dark as the same area of the original scene.
A lab that developed for you would develop the negatives and print to paper, any positives that you wanted. Any time you wanted, you could get more prints (positives) printed from the negatives.
For colour photos a similar thing happens, the negative has each of the colours inverted, light for dark, so when light shines through it it looks negatie, inverted. This light exposed photgraphic paper that darkened in that colour when exposed to light, making it back to the colour of the original scene.