Here's the breakdown:
* Shillelagh: This is an Irish word for a heavy wooden stick, often used as a weapon.
* Shake your shillelagh: This implies getting ready to use the shillelagh for combat.
It's a colorful, somewhat antiquated way of saying "let's fight" or "get ready to rumble".
The phrase is associated with Irish culture and is often used in humorous or boisterous contexts.