Catfishing is a new term for me as well, but the con game sounds all too familiar. Sometimes fakers at online meeting sites pretend to be someone they are not. They claim to be a person with more money, power, stability etc than they actually have. For example, the scammer pretends to be a model or a successful investor. This makes them seem more desirable to the people onsite whom they target.
The scammers start relationships with their targets, gain the victims' trust, then start having "problems" in order to bilk money out of their targets. Unexpected medical bills, foreclosures, financial "problems" of every description. Any con artist gains the mark's trust in order to rip them off. This online scam is just another method to accomplish their goals. The technology enables them to cast a wider net, and target more marks, than their older scams ever did.
I don't trust anyone I just met, I don't care who they are. They earn my trust over time, and vice versa. If a situation sounds too good to be true, it probably is.
There are plenty of articles about this catfishing scam on the net. Here is
one of them.