What are the essential parts of an expression plasmid, and what does each do?

Why

The origin of replication recruits the host's replication machinery and sets copy number, so a high-copy origin yields more DNA per culture while a low-copy one is gentler on toxic inserts. The antibiotic resistance gene lets only bacteria carrying the plasmid grow on a selective plate. A multiple cloning site gives unique restriction sites for inserting DNA, and Addgene's reference notes that those sites should not appear elsewhere in the backbone.

The promoter decides where and how strongly the insert is transcribed. A strong viral promoter gives high expression, while a weaker or tissue-specific one gives something closer to endogenous levels. A mammalian selectable marker, under a non-bacterial promoter, picks out the cells that took up the plasmid, and can be a drug resistance gene or a fluorescent protein for sorting.

Other common parts include a polyadenylation signal, primer binding sites for sequencing, and tags. Each choice has costs. A strong promoter can overwhelm a pathway and cause artifacts.

A high-copy backbone can be unstable with repeats. Picking the right combination for the question is most of the design work.