I've seen many times that "with+[something]+pp" or "with+[something]+ing". Could you explain this structure a little bit more?

Rebecca

"With [something] [verb-ing]" and "With [something] past participle" are additional sub-clauses to the main clause. The "with" means alongside or in conjunction with something that has happened, is happening, or someone doing something. It can also be used as the reason or cause for something. It gives a little more detail to what's already been or will be mentioned. Ex: With Jake crying in the corner, we decided to go get him some ice cream. = Because Jake was crying in the corner, we got him ice cream. Ex: The party went on for hours, with people coming and going every five minutes.