To relinquish in this case means to give up possession or control of something.

在这种情况下，relinquish的意思是放弃对某物的占有权或控制权。

I've heard that when you join Damanhur, you have to give up your possessions.

我听说当你加入达曼胡尔时，你必须放弃你的财产。

After the United States won the war they were given possession (ownership) of Puerto Rico.

美国赢得战争后，他们获得了波多黎各的所有权（所有权）。

They're telling us, " Oh, you don't have to give in your possessions, " you don't have to give in your life to them.

他们告诉我们，“哦，你不必放弃你的财产，”你不必把你的生命交给他们。