My therapist describes me (and others) in a similar way though I'm not sure about the exact term. It pretty much means what it seems to mean. It's as if there are soft spots or less thick skin, often due to wounding or trauma, so people are more sensitive to outside influences over their own affective states. "Vulnerable" comes from the Latin word that literally means "wound" so it suggests the sensitive to usually negative aspects of emotions that are stirred up.

I wouldn't worry about it as a condition or anything. It describes something about the way things work, that can either be temporary or more of a personality trait. Both of those can be changed, but it's not necessary to change it either. Having an understanding of how you're vulnerable, to what kinds of things and in what ways, can help you build up things that deal with that without necessarily changing it.