The simple high level explanation would be like this;
When you split from DAO it creates a new child DAO and pays you back your share by sending it to the new splitted DAO, (yours).
The attacker created a loop (by recursively calling the split function) caused the DAO paying several times instead of once.
Causing the DAO repeatedly (27996 times) transact the amount of 237.62451099999999 Ether to the new child DAO.