Double entry bookkeeping is an accounting methodology introduced in the 13th century to to make sure that each transaction and account is properly balanced. It greatly reduces the likelihood of data-entry errors.
A double-entry transaction is a transaction that contains entries for two (or more) accounts that balance against one another. One account is debited by an amount equal to what the other is credited. By ensuring that each transaction balances, a balanced set of accounts is guaranteed. This doesn't totally prevent errors, but it does eliminate the class of "I forgot to enter that part of the transaction" errors. In the course of maintaining large, complex sets of accounts with many transactions, it is very easy to make errors that may go undetected for a long time, and be appallingly difficult to track down, even when double-entry bookkeeping is used.