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