If vehicles and other machines conk out, they stop working or fail suddenly.

I was just two miles from home when my motorbike conked out! 我出门刚骑了两英里，我的摩托车就突然出了故障！

to go to sleep very quickly, or to suddenly become unconscious

After a six-hour flight and a long day of meetings, it's not surprising you conked out. 坐了6个小时的飞机，又开了一天的会，难怪你倒头就睡着了。