It is difficult to answer without more context; however, here are some speculations:
First of all, "erupt" is the word used for when a volcano begins shooting fire and molten lava into the air. In this scenario, the girl was about to "erupt" with laughter (or "explode" with laughter).
Second, the girl might just think it is funny that the other person at the restaurant thought they were someone they were not. Or, depending on the rest of the story, Sid and Nancy could be other characters in the story. In that case, the girl simply thinks it is funny that the person in the restaurant would think they were Sid and Nancy. However, there is no underlying meaning behind "Sid and Nancy" that I can see.