BreadcrumbList (schema.org)
BreadcrumbList is the schema.org type that marks up a page's navigation path in machine-readable form, say home page, category, subpage. Each step of the path is a ListItem with the properties position and name; item carries the URL and may be omitted on the final step. Search engines read from it where a page sits in the website structure. Google can show this path in search results in place of the bare URL. Valid markup does not guarantee that display; whether it appears is Google's decision per query. The markup sits in the page head as JSON-LD and describes the same path the visible breadcrumb shows. Where the two diverge, the markup makes a claim the content does not back.
In practice
In practice the markup should not be written by hand but derived from the same source as the visible breadcrumb – otherwise the two drift apart. Google recommends a path that reflects a typical user journey; the home page and the current page may be included, but neither is required. position counts from 1. The markup earns its place above all where pages sit deep in a structure, such as category and glossary pages. The Rich Results Test shows whether Google reads the markup. Only the page itself shows whether it matches the visible breadcrumb.