How much a gene is actually transcribed into RNA — a mutation can't become a neoantigen if the gene it sits in is silent.

DNA is the blueprint; expression is whether (and how much) a given gene is read out into messenger RNA and made into protein. RNA-seq measures this transcript abundance genome-wide, giving a per-gene expression level.
Expression is a hard filter on neoantigen candidates: a beautifully predicted, well-binding peptide is worthless if its gene isn't expressed in the tumor — no transcript, no protein, no peptide to present. Pipelines routinely intersect the somatic-mutation list with RNA-seq so that only mutations in expressed genes survive to the ranking stage.