Why are two forward and reverse priming sites depicted here? what do they do?
It's just extra information that you don't need to understand the part above. You could use these primers for colony PCR or sequencing when you'd use the plasmid (after transforming to E.coli for example), but they're not absolutely required. 

Compare it with this map for example. There are also some primer sites listed, but you don't actually need those primers for anything.