Hardliners are the people in any government or regime who support strict, inflexible, orthodox adherence to the prevailing ideological system. They are, in other words, the "true believers." The softliners, on the other hand, are the regime-supporters who are more flexible and pragmatic.
The great advantage of dictatorship is that because one person is making all the decisions, it is easy to get things done—as long as the dictator wants them done. The downside of a dictatorship is that one person (the dictator) is unlikely to see all sides of a situation. A dictatorship can easily become so rigid and so blind to the needs of certain groups that this can undermine the stability of the regime.
Softliners can run interference, mediating the gulf between the dictator and his inside cohort and other, more marginalized groups, and, therefore, they are able to help moderate the harshest edges of the regime. They are a group trusted enough by the regime to have some influence, yet they are not blindly ideological: they can breathe some air into a system that might not be able to make the changes needed to survive otherwise.