Think of ID as a global variable, the first time you "declare" its value, this value is set througout the document and will "render" the given value anywhere you call the ID.
"@id": "http://example.com/" *here you give ID a value*
"@id": "http://example.com/", *here you just "paste" the given value*
"name": "Lecture 12: Graphs, networks, incidence matrices"
That's why you literally get a full URL within a breadcrumb trail.
In fact IDs should be VERY consistent domainwise in order to disambiguate entities and actually spare the effort of having to declare one time and another the same thing, like repeating several times a homepage URL or very likely a postalAdress if you do content about LocalBusiness and other types of Organization.
A big benefit is that other authors may reference this ID from extrnal sites/domains and even then this will be an univocal relation. Think big, kinda semantic link building (out of scope, just an example of possible use).
You can find a working example in ZeClinics contact page where I am hashing the 2 premises of the company in order to set a precedent to be recalled in future RDF and onpage Schema developments.
Furthermore, if you are using CMS for website maintenance I would perhaps advise to implement Breadcrumb with RDFa (my favorite vs Microdata) and keep this trail apart from the far more flexible (and thus complex) JSON-LD scripts.
This is absolutely common in many WP themes, for example.