A certificate of analysis is the document a testing lab issues after it tests a sample from a batch. For research peptides it usually states the compound tested, the batch or lot number, the test methods, the purity found by HPLC, the identity confirmed by mass spectrometry, the test date and the lab's name.
A COA only proves something about the batch it names. Buyers increasingly check that the batch number on the report matches the number on their vial, and that the lab can confirm the report independently.