The term's origin is quite literal. In ancient China, a string of 1,000 coins was a full “diào”. Half a string, or 500 coins, was a “bàn diào”. This term was used metaphorically to describe a person who was not “all there”—intellectually or skillfully incomplete, as if they were only worth 500 coins instead of the full 1000. This image of being “half a string” perfectly captures the modern meaning of being incomplete or half-baked.
`半吊子` is an informal and very common term. Its connotation is almost always negative, but its harshness depends on the context.