ACID properties are an important concept for databases. The acronym stands for Atomicity, Consistency, Isolation, and Durability.
The ACID properties of a DBMS allow safe sharing of data. Without these ACID properties, everyday occurrences such using computer systems to buy products would be difficult and the potential for inaccuracy would be huge. Imagine more than one person trying to buy the same size and color of a sweater at the same time -- a regular occurrence. The ACID properties make it possible for the merchant to keep these sweater purchasing transactions from overlapping each other -- saving the merchant from erroneous inventory and account balances.
Also see concurrency control and locking.
More detail for the current topic: ACID Properties
More on the general topic: Basic Concepts for Using a DBMS