What was the meaning of Fiona's visit to the killer in prison, in the last scene?

It ends the film with a message of hope and forgiveness.

Throughout the film, Father James is struggling to communicate with the residents of his town who have grown cynical and weary of God, particularly in light of the sexual abuse crimes perpetrated by members of the Catholic church. He also has a hard time connecting with his daughter Fiona, who's recovering from a suicide attempt and feels her dad has abandoned her.

But the very final scene shows us that all communication is not lost. Fiona is compassionately willing to talk to her father's killer, something her father tried to do with his parish throughout the film. And the killer, who at the beginning enters the confession booth not to talk but rather to tell the priest he's going to kill him, is now sitting in yet another room with a divider - but makes a different choice. Says Brendan Gleeson who played the lead role:

[Father James] lives on in his daughter. They have connected even though he abandoned her twice. And [the killer] picking up the phone wasn’t a foregone conclusion. But having him do that has us staring up at the end of the film rather than down.

Says the film's writer and director, John Michael McDonagh:

I also wanted it to end on a moment of hope. I felt the film was somber enough. I wanted the final shot to be kind of a grace note. One thing I did change to make it more hopeful was when she motions for the killer to pick up the phone. In the original draft he doesn’t, but again, I wanted the film to end on a much more hopeful aspect. [...] [The killer has] destroyed the priest, but he’s also destroyed himself. But by picking up the phone, he may have still saved himself.

I have to whole heartedly disagree. Not just because of the above quotes from the director but it’s obvious throughout the film, the daughter never ‘returned’. She’d in fact never been there before. She hadn’t seen her father since he left.

The conversation preceding the final scene about virtues being more important than sins led me to believe she went to forgive him. She arrived broken and somehow through tragedy found virtue in herself.

It is of course just my opinion. Your interpretation is interesting though. I just don’t see it.

Think its patently obvious , the daughter is the lover of the killer and is the instigator of the crime during which she killed her fathers dog

She was in a abusive relationship which is why she came back . She also told us how her father had hurt her badly by leaving and despite saying she forgave him the underlying emotion was that she hadnt . The killer was an abuser as per his wifes face and it is no coincidence that he confessed to his intention as the daughter returned .The burning of the church is understandable to bring the priest pain and suffering but the dog is out of kilter with it and probably only the daughter knew of the intense relationship between the dog and its owner . She knew the killers intention and left before it happened but there is no other reason that I can see why she would visit the jail with almost a smile on her face with no despair or anguish over her fathers death . QED