1. Literally, in a deep part of a pool or other body of water. The kids were in at the deep end of the pool when Timmy started having trouble staying afloat.

2. In a particularly troublesome, difficult, or dangerous situation, especially one from which it is difficult to extract oneself. Though we were the newest army recruits, we found ourselves in at the deep end when our squad was sent to the front lines of the battle. As my small gambling habit became an addiction, I was soon in at the deep end of an insurmountable debt.