As other users told, 折る is a transitive verb that requires an objective such as 折り紙を折る － do an origami. 折れる is an intransitive verb, like 箸が折れる chopsticks snap. It requires a subjective.
折る、折れる aren't necessarily referring to physical objects like a branch, tree, bones, and a window glass. It can be used for abstract objects, for examples:
骨を折る - make an serious effort, take care of (someone else)
話を折る - interrupt others' story, stop other's talking.
腰を折る - block / check someone's attempt
心が折れる - discouraged, down-hearted