a whip, and the flogging carried out with it
This is the plain, physical meaning of the word: a whip, and the act of beating someone with it. In the Roman world the whip in view was a brutal instrument, often several weighted leather thongs braided together, and being flogged with it was used both as a punishment and as a way to force a confession out of a prisoner.
The New Testament uses this literal sense in two settings. In Acts a Roman officer is about to have Paul beaten in order to interrogate him, until Paul reveals he is a Roman citizen and stops it. In Hebrews the word appears in a roll call of faithful people who endured floggings rather than give up, language that deliberately recalls Jewish martyrs tortured for their faith. A closely related word is the temple whip Jesus made (φραγέλλιον), and the verb for the act of scourging is μαστιγόω.