Instructions
Insert the memory card you want to format into a memory card port with the PS2 turned off. Make sure there isn't a disc in the console.
Turn on the PS2.
Select the "Browser" option on the "Main Menu" screen and press X.
Choose the memory card icon, and all the files stored on the memory card will appear on-screen.
Use the directional pad to highlight all the files on the memory card, then choose the delete command to clear the memory card.