Sole parental responsibility means that the major decisions for your children are being made by one parent only. This could be due to domestic violence, abuse, neglect, a parent not willing to make decisions or difficulty communicating.
This does not mean that the other parent is not involved at all in making decisions or that they are not informed. Sole parental responsibility orders can include requirements for notifying the other parent of the decisions to be made, asking for their input and consideration of the input however, the ultimate decision is left with one parent.
Whilst it is not rare for sole parental responsibility to be ordered it is not a simple order to obtain from the Court.
If any of the above applies to your circumstances make sure you are seeking advice about this issue early in your separation.