Visitors are bound to their server calls by their Visitor ID (at least), which is a part of each server call
How are server calls parsed into visits? Is there a marker or a unique ID for the visit on each server call? Or are server calls aggregated into a visit on Adobe's side?
Yes, for a particular visitor.
To be more technical it is the ID through which the visitor is identified for the hit. This ID is a combination of post_visid_high and post_visid_low.
Here is the document that provides the information on the various methods used to identify the unique visitor:
Here is how visits can be calculated from raw data collected by Adobe:
So it's those 4 rules in combination with what? The visitor ID?
There are 4 rules that are used to combine hits into a visit