I'm sure you may have quarreled with your friends or family members in the past. As time went by, you decided to end the silence and made an apology to put an end to the misunderstanding. The idiom, to extend an olive branch means to make peace by ending a fight or a misunderstanding with your dear ones.
When you have a tiff with someone, you stop communicating and drift apart from them. Sooner or later you realize your mistake and decide to put the past behind by starting afresh with them. When you apologize and make peace, it means you are extending an olive branch.
So when you put an end to the existing conflict and bring peace in your relationship, it means you forgive and forget by extending an olive branch to them.
It is a symbol or token of peace made to someone, in order to have a smooth relationship with them.
Example 01 : After the big argument, Sam realized that he couldn't stay without talking to his girlfriend, so to bring things back to normal, he extended an olive branch to her.
Ex 02 : When Chang learnt that he would be working with Michelle on the new project, he was forced to extend an olive branch to her , keeping his personal differences aside.
Ex 03 : When Suzan realized that her children were badly affected with her daily arguments with John, she extended an olive branch to him.
Ex 04 : The factory owner extended an olive branch to all the employees on protest, by giving into their demands, to resume the halted production.
Ex 05 : The Manager extended an olive branch to his team member, when he realized that he had over reacted by screaming at her for a small mistake.
Ex 06 : Rosy tells Peter, " Your girlfriend lied to you, she is at fault, why should you apologize ? Let's see if she extends an olive branch to you."
Ex 07 : The famous actor extended an olive branch to all his fans for being drunk and misbehaving publicly in the stadium.
Ex 08 : Peter advised William to write an email to his boss and extend an olive branch for absconding from work without prior intimation.
Ex 09 : To bring the family dispute to an end, John extended an olive branch and invited his family over dinner to start afresh.
Ex 10 : When the customers were displeased with the food served to them, the chef extended an olive branch and compensated by replacing the dish.