1. In detail: This is the most common meaning. It means to discuss something thoroughly and comprehensively, covering all aspects of it. For example:
* "The professor explained the theory at length."
* "She described her trip to Paris at length."
2. Finally, after a long time: This meaning signifies that something happened after a period of waiting or delay. For example:
* "At length, the train arrived at the station."
* "After a long wait, the meeting finally began at length."
The meaning of "at length" is usually clear from the context. If you're unsure, it's always best to consider the surrounding words and phrases.