It helps to give context and a source citation in questions like this. With some research I identified the source of the quote as Torre-Ubieta, "Advancing the understanding of autism disease mechanisms through genetics".
The quote comes from a section of the paper discussing the main two different genetic models of ASD: (1) the polygenic (many genes contributing small influences) model, and (2) the major gene model, where a variation of a single gene is responsible. The first two sentences of the paragraph having the quote are:
The unified major gene model62,63 is supported by the significant increase in damaging de novo mutations found in subjects with ASD as compared to their unaffected siblings44,49. Further support for this model is seen in the phenomenon that there are more inherited SNVs that disrupt protein function in conserved genes transmitted from the mother to individuals with ASD than in unaffected siblings73.
The sentence in question (the first) is simply citing evidence supporting the second kind of model; it is not claiming that the majority of risk is due to de novo mutations. As to how de novo mutations support the major gene model, it helps to consult the papers cited in the sentence. Review of citations 44 and 49 show that those with ASD often have rare de novo mutations that look to be gene-disabling, whereas their unaffected siblings do not. This suggests that disabling of a single gene can bring on ASD, and thus fits with the major gene model, but does nothing for the polygenic model since it supposes one gene difference has only small effect.
Let me add that the two models are not mutually exclusive: a polygenic model might explain the observed familial occurrence of ASD, while a de novo major gene model might explain why only a few in a family are affected.