NP-hard - Definition The definition of NP-hard problem in Wikipedia is :
NP-hardness (non-deterministic polynomial-time hard), in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP".

There are NP-hard problems not in NP class. My question (more curiosity) concerns the NP in the definition. Since a NP-hard maybe is not in NP class, why we call it NP-hard? 

When we say we have a NP-complete problem, then this problem is indeed in NP class.
Here is a definition which describes the relationship between hard and complete:


  Given a set C of problems and a reduction R, it is natural to ask if there are problems Π ∈ C such that any problem Π′∈C,  R-reduces to Π. Such “maximal”
  problems are called in complexity theory complete problems. Let C be a class of
  problems and R be a reduction. A problem Π ∈ C is said to be C-complete (under R-reduction) if for any Π ∈′ C, Π′ ≤R Π. A C-complete problem (under reduction R) is
  then (in the sens of this reduction) a computationally hardest problem for class C. For instance, in the case of NP-completeness, NP-complete problems (under Karp-reduction) are the hardest problems of NP since if one could polynomially solve just one of them, then one would be able to solve in polynomial time any other problem in NP. Let C be a class of problems and R a reduction. A problem Π is said to be C-hard (under R-reduction)
  if for any Π ∈′ C, R Π≤ Π ′. In other words, a problem Π is C-complete if and only if Π ∈ C and Π is C-hard. 


References


An Overview on Polynomial Approximation of
NP-Hard Problems
Computers and Intractability: A Guide to the Theory of NP-Completeness