What does this mean

"Hak" means right.
in religion of Islam people have rights on eachother. Specially people you live together (friends, parents, brothers/sisters, partners, etc). People when they are living together can do bad behaviour or good behaviour.
So "Hakkını helal et" means "if i did behave badly to you please forgive me (pardon me)" sometimes means "Pardon me and farewell"
I hope I could express it.

Gençtürk is right in how it is used.

My friends explained to me that in Islam God only forgives sin against another person if that other person is prepared to give up their rights to see God give retribution.

Hakkını helal et is used quite regularly in the following circumstances:

1. I know I have upset you, and I want you to forgive me.

2. I am going away/ leaving school / changing job etc. I don't want anyone at the old place to hold a grudge against me.

3. Invitation by the imam at a funeral. Everyone in the crowd of mourners shouts out with one voice 'Yes we give up our rights'. THIS IS VERY IMPORTANT as it shows publicly that you hold no grudge against the deceased, and so Allah can accept them into heaven. In fact doing this is called you "son görev", your last duty towards your loved one.

You probably wouldn't hear Hakkını helal et it used for giving up your rights in any non-religious sense. (e.g. to give up rights over property in a divorce, to give up your right to go to university). Then Hakkından vazgeçmek would be more usual.

So it makes a bit of a nonsense of looking up definitions in the dictionary then.But thanks.