Great question!
MCID is a web technology that is used to ID a logical device (browser cookie) across multiple Adobe solutions. For example a single visitor should have the same MCID value across Target, Analytics, AAM, and other web based Adobe solutions. This allows things like A4T, Audiences, and other Core Services to work correctly.
A declared ID/Customer IDs are a ID that you set based on knowing the visitor. For example, you might set a declared id of a hashed CRM ID after the customer logs into your website. This is an ID that you might know about that visitor to connect offline data.
Adobe Campaign obviously doesn't use cookies since it's primarily works through emails. Using a declared ID here is more practical than trying to retrieve a cookie value from a webpage.
I've also tagged our Campaign community manager here incase he has any additional context
florentlb - Anything to add here?