A prison record was a record of one's stay in a prison.
According to Cardassian prison records, Kira Nerys spent a week at the Elemspur Detention Center in 2361, though Kira had no memory of it. When discussing the discrepancy with Odo in 2371, he told her that either the records or her own memories had to be wrong. (DS9: "Second Skin")
While General Martok perused the IKS Rotarran's personnel reports in 2373, he commented that they sounded more like prison records. (DS9: "Soldiers of the Empire")