can someone explain how "campaign is requested" works?

You can also think of a requested campaign as a sub-routine to the main smart campaign.  The important point to realize though is the requested campaign runs in parallel with any additional flow steps contained in the parent campaign (it doesn't run like a true sub-routine that first completes before any additional logic/flow steps are run in the parent campaign).  So you may need to get creative with wait steps if you want the requested campaign to finish running before continuing on with the flow steps in the parent campaign.

Another good use-case for requested campaigns is for repeatable logic/steps that many campaigns can refer to - rather than build the same logic within each smart campaign that needs it.  We have a single "sync to CRM" smart campaign that has all of the required logic - in our case, assign leads to country marketers based on country value.  And every smart campaign in our lead lifecycle program that would otherwise have these sync rules as additional flow steps within the campaign - now can simply request this central smart campaign whenever needed.

Here's the central "Sync Lead to CRM" smart campaign:

And one of the many smart campaigns that requests it as part of the overall flow:

As you you can see, this is a very scalable approach and makes maintaining the lead owners very easy since it's only done once.