Imagine you have a toy camel that can carry a lot of straws on its back. However, if you keep putting straws on its back, it will eventually get too heavy and break.
That's what happened with the camel's back. It was already carrying a lot of weight and then one last straw was added, and it finally broke.
The straw that broke the camel's back means that this one little thing was the final problem causing the situation to become too much to handle.