What does it mean for a problem to be both NP hard and coNP hard

Question

I have a faint notion of what NP hard is (that a problem is legit difficult 3 SAT for example).

I have forgotten what coNP hard, and Wikipedia tells me that the complement of coNP hard is NP hard...not really helping there

Can someone please clarify for me on an intuitive level what does it mean for a problem to be coNP hard? Further, what does it mean for a problem to be both NP hard and coNP hard? What is a problem that illustrate this concept?

Thank you!