ACID stands for Atomicity, Consistency, Isolation and Durability. In a database server with many simultaneous connections, problems might arise if some process changes data between the time an application has searched for it and tries to act on it. ACID-compliant transactions ensure that processes cannot interfere with each other, and that data remains in a complete state.
MySQL offers ACID-compliant transactions with the InnoDB engine, and the upcoming Falcon engine. See http://dev.mysql.com/books/mysqlpress/mysql-tutorial/ch10.html
This was first published in April 2007