扬鞭 is a literary verb-object phrase meaning 'to flourish or raise a whip', often used in classical poetry, martial arts fiction, or formal writing to evoke a vivid image of setting off on horseback with determination. It is a separable verb (离合词): the object 鞭 can be modified or separated from 扬, as in 扬起鞭子 ('raise the whip'). You won't hear it in everyday conversation — it belongs to written or rhetorical registers.