First of all I am of course aware of the wikipedia article: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem
However I still do not understand exactly what the problem is. To demonstrate that I've tried, I think it is as follows but I am not sure:
The problem of checking whether a given boolean equation with k distinct variables is satisfiable.
For example, is this an instance of the 3-sat problem?
x OR y OR z