Depends who is making the threat and in what context.
"Better safe than sorry"
Please be careful. I advised you based on what you said. You never know... if I have more information I might tell you it is nothing.
If they are on-line then they are stupid
What are the threats? by whom are you being threatened?
both. trust your instincts, and be careful
If they are 6' 6" tall, serious. Seriously though, you need to consider the person who is threatening you. Don't lightly disregard a threat, or let every threat frighten you. Consider the source.