When someone is said to have emotional problems what does that actually mean?

"Emotional Problems" I agree with dr. Chen and the possibilities he raises. But this term is so wide it defines little, and you would need to ask the speaker what s/he means. There are myriad ways that we can experience, display, and respond to hurt -- often resulting in behaviors that we later regret. That said, we've all known people who go "off" with little provocation -- or maybe we even are that person!
Emotional problems. I think many people are referring to a person not being able to regulate their emotions and/or behaviors without chaos, conflict or hurt and pain (for themself and/or others).