'binary-labeled' is a modern English compound formed from 'binary' (originating from Latin 'binarius') + 'label' (from Middle English/Old French 'label'/'labellum'), with the past-participial/adjectival suffix '-ed' added in English.

'binary' comes from Latin 'binarius' meaning 'consisting of two', which entered English via Late Latin and Old French as 'binary'; 'label' developed from Middle English (from Old French and ultimately Latin 'labellum' meaning 'small tablet' or tag). These elements combined in contemporary English to form compound verbs/nouns such as 'binary-label' and the past/adjectival 'binary-labeled'.

Individually, 'binary' originally meant 'consisting of two' and 'label' meant 'a tag or marker'; together, and with '-ed', 'binary-labeled' has come to mean 'marked or categorized into two classes', a usage driven by modern data-science and classification contexts.