This is common with eels (as they seem to be). They tend to keep wriggling LONG after they're dead. They're not the only fish to do this either, but I think they are the most extreme example.
I've experienced the phenomenon myself once, although not with eels. My father and I went to the local harbor to buy some fresh fish directly from one of the returning fishing boats. We bought three
European Flounders and brought them home. We then cut off their heads and gutted them, and left them in a bag on the kitchen table for later. Well, we quickly had to move that bag, because they kept thrashing around so much that they knocked everything else off the table, so we had to hang the bag on a doorknob. They still kept thrashing about for several hours afterward. But they tasted great :-)
Here's another guy's experience with preparing eels:
http://neilcooksgrigson.blogspot.com/2009/10/next-simply-prepare-your-eels.html Navagon: Perhaps amazingly, a Youtube commenter had the intellect required to address this:
I think it is the lemon juice that creates this phenomenon. The muscle cells react to the acid in the juice.
No, eels just do this.