A component of ACID; Atomicity is a property of a unit of work (e.g., a transaction) such that the separate operations of the unit of work are either all performed, or none of them are performed. Simply put, atomicity means "all or nothing".
A transaction that exhibits atomicity is said to be atomic.
In other words, an atomic group of sub-tasks, --no matter how many individual tasks the group is composed of-- will be atomic if all the sub-tasks in the group are handled as a single group-task. The group-task is only completed when all the member tasks are successfully performed. If one or more of the member-tasks are not performed successfully, then the system will left in the same state it would be in if NONE of the member tasks had been performed.
Example: if entering a credit card sale is composed of three distinct steps (1. swipe, 2. key in PIN, 3. accept amount) then the transaction should be performed atomically. That way, if the swipe machine shuts off after the first step (swipe) is complete, the transaction will not be performed at all. Thus, there will be no partially completed transaction in the database tables to deal with.