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."
Someone who reveals all their emotional baggage to anyone who will listen. Relates to someone who talks about all their problems--especially in dating and love--on a first date.
Sarah and John will not be going on another date because she was an emotional slut on the last one. She told him all about her failed relationships, problems with her boss, and how her cat keeps throwing up. She cried; he left.