This is an expression that is used to refer to someone who thinks very highly of himself. When you say that someone is too clever by half, what you mean is that the individual is very annoying because he imagines himself to be much smarter than he actually is. You are implying that he is much too clever for his own good, and this might get him into trouble one day. The expression is mostly used ironically. It is also possible to say ‘too smart by half’.
*You should meet the characters in my class. Some of them are too clever by half.