When the wearer fights in a challenge, he must 'swap' the Strength, Toughness, Initiative and Attacks characteristics on his profile with his enemy (but not the enemy's mount, if he has one). So, the wearer fights with his enemy fights Toughness, Initiative and Attacks whilst his enemy fights with the wearer's Strength, Toughness, Initiative and Attacks.
Note that you cannot choose not to use Van Horstmann's Speculum and you must swap all of the listed characteristics for the duration of the challenge, not just some of them.