operationrainfall.com/wp... Curly is a robot, and she's named after this character: "{". In north american english (and amongst programmers) this is called a curly brace, though it has other names
My degree is in Computer Science. In my domain, curly braces are most commonly seen in programming languages that descended from or were inspired by C (including java, c++, javascript, and hundreds of others)
Cave Story was written in C++ by Pixel, who also did all the writing, art, and music. He almost certainly named her (and her partner quote) with a mind to their use in programming.
In C (and C++), curly braces mark out statement blocks (groups of instructions). These languages are "lexically scoped", meaning that variables defined inside curly braces only exist there.