I think the phrase "shot noise" was introduced by the developers of DESeq. I think it refers to the statistical variability in read count which is purely due to the sampling process of reads from, say, genes. For example (nothing to do with NGS) you flip a coin 100 times, you expect 50 heads, 50 tails. In practice you obtain counts of heads slightly different from 50 even if the coin is perfectly balanced (in biological context you would say there is no biological effect). That variability is purely due to chance and is called shot noise.
With low read counts the shot noise can make up a large proportion of the variability but for high read counts it becomes negligible (image flipping a coin just 10 times as opposed to a million, in the latter case the difference from 50:50 is tiny). So for an RNAseq experiment where you can easily (cheaply?) get 1000s of reads per gene and the shot noise becomes very low, there is no point in sequencing the same library really deep, much better is to sequence more libraries at moderate depth (say ~10million reads each for a typical experiment).