The simple high level explanation would be like this; 

When you 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.