Dickens characterizes Oliver's father as having fallen in love with Agnes, Oliver's mother.  In true Dickensian fashion, this love is interrupted by the pursuit of economic wealth.  A relative died in Rome, having left to Edwin Leefold a great sum of money.  He had to travel to Rome to settle the will and then, presumably, would return home to be with Agnes, the woman he loves.  A day after landing in Rome, Oliver's father contracts an illness and dies.  

Oliver's father did not abandon Agnes.  While her giving birth to Oliver in the opening of the book certainly feels of abandonment and is complete with the doctor noting "no wedding ring," this is not the case.  Dickens has been able to construct a setting in which characters like Agnes and Edwin have deep feelings for one another.  However, their subjective feelings are overcome by material reality.  The dominance of material reality and how it influences people, almost overcoming their own emotions, is a major part of the narrative and is evident in why Oliver's father left his mother.