Mental preparedness for potentially emotionally messy situations, i.e. a one-night stand after a breakup, a confrontation with a friend, coming out of the closet. An emotional condom is the mental parallel to the physical condom - an actual condom keeps your sexual organs from getting damaged, an emotional condom keeps your heart and mind from getting damaged.
"You're going to hook up with him? Fine, but remember to put on your emotional condom."