Henchmen are hired Wizards that help you in a duel and they can only be purchased during your turn while you are in combat. They will come to your aid and behave similar to your Minion, only stronger and smarter. They will act in the same round that they are summoned by the player, and will disappear once the duel has ended.
If the Crown shop is loading slowly for you, and doesn't give you enough time to buy a Henchmen during your turn, change your settings to LIST view (as opposed to ICON view) for faster loading.
If you're having graphics problems, another thing you can try is to set "Smoothing" to "Crowns Shop".
Henchmen cost Crowns. If you don't have Crowns, you can't hire any henchmen. As said, you can only hire henchman after you start or join a battle. Once you buy/hire one, your spell timer will revert to 30 seconds, and it will do so after each additional one you buy.