Some Christians believe that moral truth is absolute because it is defined by God. Some regard morals as a reflection of God's un-created eternal nature. Many people who are not Christians believe that morals are defined by culture, society, family, and reason thus making morality relative rather than absolute. It may seem an easy question to settle if one is a committed member of either group yet the way people behave points to both absolute and relative morality in their thinking and in their motivations. Is morality totally absolute? It it totally relative? Is it a combination of both? And how is it one, the other, or both in the system of beliefs and way of life that you espouse?
If there is no absolute morality then nobody has any right to say that what I do is right or wrong. In the absence of some objectively defined morality nobody has the right to tell me it's wrong to shoot my neighbor for parking inconsiderately, nobody has the right to tell me it's wrong to mug an old lady to steal the money she just took out of the bank, nobody has the right to tell me it's wrong to sleep with someone else's wife, and so on. Their insistence that it's "wrong" would be no more and no less valid than my insistence that it was just fine.
Many people who seem to like the idea of relative morality soon seem to struggle with the idea that, in the absence of an objective moral standard, nobody has the right to say that the likes of Hitler or Stalin or Pol Pot were evil because under a totally relative morality they were merely living under their own moral codes which are no more and no less valid than anyone else's. They just had enough power and influence that their moral codes had an impact on a lot of people.
But then we get into the real kicker, if there is an absolute morality who gets to define it, and under what circumstances might it be varied? We might say it's absolutely bad to kill another human being but it's not difficult to come up with scenarios where any one of us might do just that. Most people wouldn't shoot their neighbor for parking inconsiderately but what of the intruder who would abuse our daughter unless we took drastic action to prevent it - how many of us would squeeze the trigger and end their life to protect our daughter? Likewise we can say that theft is wrong but what about the person who steals for no reason other than to eat? I believe there was a court case in Italy recently that acquitted a man who stole a single loaf of bread because he said he needed it to feed his family.
So on that basis I think we would have to say there are some absolute rules, but at the same time there are arguably instances where the absolute rules need to be considered in context and possibly broken. But then of course we get into a question of who gets to decide when it's acceptable to break the rules, and if we go down the "least harm" route we potentially reach a place where a healthy person can be killed so their organs can save the lives of a dozen other people.