A question in article

[Jiyishuai]

Dear Taner Arslan:
I am so admiring your fancy analysis work in the article Proteogenomics of non-small cell lung cancer reveals molecular subtypes associated with specific therapeutic targets and immune-evasion mechanisms Nature Cancer. But I'm quite confused about one of your analysis methods: Enrichment analysis of the overlaps of six proteomic subtypes with previous subtypes, which are visualized by Volcano plots (such as Extended Data Figure 2a,b).

What do the y-axis, x-axis, and dot size mean? And What R function could be used for those? It would be greatly appreciated If you could explain this volcano plot. Or could you please share your analysis code and data? 
Looking forward to your reply.