WHEN HE MET his father’s eyes from across the crowded hall, Amar understood that an agreement had been made between them: they knew who they were there for, and why they would not approach one another beyond the expected salaam. Amar looked away first. He still felt it. His anger, and the distance it caused. It was as if something had clenched in him and could not now be loosened.
Without more context it's not possible to be definitive, but here goes.
It sounds like Amar and his father have had a huge argument and are still very angry at each other. They would like to start shouting at each other and continue the argument.
However, the person 'they were there for' - the reason that they are where-ever they are - would be upset at this (possibly they are at Amar's sister's wedding for example) and do not want to upset them, so they won't speak to each other beyond the minimum expected civilities.
When you go to any gathering, there is sometimes one person who makes you accept the invitation. I went to my brothers wedding although I didn't know his wife nor any of his friends (it was an odd situation, but never mind); I was there for my brother because he wanted me there.