What is the meaning of the idiom "a hard nut to crack"?

The idiom "a hard nut to crack" means a difficult problem. It is a metaphor that compares a difficult problem to a hard-shelled nut that is difficult to open. The idiom can also be used to describe a person who is difficult to understand or deal with.

The other options are incorrect. Nuts which have a hard shell is the literal meaning of the idiom, but it is not the idiomatic meaning. A dreadful disease and to break a promise are not related to the idiom in any way.