What is an instance of NP complete problem?
Other answers are good, I'll give only another trivial example:


problem: "given two numbers $k,n$ with $1 &lt; k &lt; n$, does a number $m$ smaller or equal than $k$ exist such that $n$ is divisible by $m$ ?"
the instances of the problem (or informally the input of the problem) are all the valid pairs $(k,n)$ such that $1 &lt; k &lt; n$; so $I = \{ (2,3),(2,4),...,(3,4),(3,5),...\}$
the set of solutions is the set $S = \{ YES, NO \}$, indeed the problem is a decision problem (the answer to the question "does exist ...?" is simply YES or NO)
the abstract problem $Q$ is a subset of $I \times S$ and is the relation that associates an instance of the problem to the correct answer


So:

Q = { ( (2,3), NO  ),
      ( (2,4), YES ), 
      ( (2,5), NO  ), 
      ....
      ( (6,13), NO ),    
      ( (6,14), YES ), 
      ...
      ( (7,13), NO ),    
      ( (7,14), YES ), 
      ...
    }


P.S. the problem $Q$ is known as INTEGER FACTORIZATION and probably you'll meet it again ... :)