Something that's verifiable can be proven. In a courtroom, verifiable evidence is backed up with specific proof.
If you have a birth certificate, your exact time and place of birth is verifiable — in other words, you can prove where and when you were born. Something is scientifically verifiable if it can be tested and proven to be true. Verifiable comes from the verb verify, "authenticate" or "prove," from the Old French verifier, "find out the truth about." The Latin root is verus, or "true."