Well I'm no Scholar but I do know that if you forgive someone for their wrong against you and they ask God for forgiveness as well then they are forgiven. Also if they ask you for forgiveness and you refuse to forgive them no matter if you forgive them or not. They ask God for forgiveness they are still forgiven but you are the one holding onto the sin and it will eat you up but the person who asked for forgiveness is free and clear. What does it mean to you? I will have to go home and read the verse and examine it more deeply.
Okay. Same thing, just an opinion. But I've definitely got that Catholic perspective.
Before we ever get to the 'how does it apply in our lives' meaning, what is John telling us that Jesus is doing on that evening? What is going on between Him and those particular persons? He's not speaking to the crowds. And He's already appeared to the women at the tomb and the disciples on the road to Emmaus and He hasn't said anything like this.
To me, it looks like He is sending the disciples to exercise the authority to forgive sins that belongs to Him. Preceeding this He says, "As the Father has sent me, so I send you."
The authority and ability to forgive sins remains God's alone and these particular human beings are one way He chooses to exercise His forgiveness.
Just an opinion, of course.