A Difficult problem is one that has no efficient general solution or algorithm. Some problems are Difficult because no efficient algorithm is known to solve them, for example the Traveling Salesman problem?. Others are even more Difficult as there is no known solution—or, even worse, it can be proven that there is no general solving mechanism. Theorem proving, for example, is Difficult in the second sense.
The most frustrating limits are those walls put up by Difficult problems. I am constantly bumping my head up against constraints? in language design. Constraints are quite natural ways to describe problems, but finding a way to satisfy them is Difficult.