It's an internationally standardised attachment to your university diploma, listing the courses you took, grades, credits, and a brief description of the program. It's issued in English (and the local language) by your university.
When you want your degree recognised abroad, a diploma supplement saves a lot of back-and-forth about what subjects you took and how the program was structured.
"To apply for a PhD in Cesena, Mai-Lan asked her old French university for a fresh diploma supplement in English. The Italian institution accepted it together with her transcripts."
Not every university issues it automatically. If yours doesn't, you may have to request it specifically and wait a few weeks for delivery.
Official source
European Commission
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