To be "too smart by half" (also common is "too clever by half") is to be too smart for one's own good, meant either literally or ironically. As an idiom, it is usually sarcastic. The phrase has a wide range of potential uses; for instance, it can mean:
1.) Something so complex that it's self-obfuscating.
2.) A seemingly clever action that is in fact foolish.
3.) Logically accepting something as necessary that isn't.
5.) Elitism (see ivory tower