Parental responsibility is basically about making major decisions involving the health, education or welfare of your children.  The presumption is that the parties will share parental responsibility, which means that important decisions should be made only after thoughtful discussion between both parents.  This does not mean that the parties must agree about every decision involving their kids, but it does mean that some form of discussion should take place.  Ultimately, the primary residential parent has the final say regarding any child-related decision that must be made.