Data inconsistency refers to whether the same data kept at different places do or do not match.
Point-in-time consistency
Point-in-time consistency is an important property of backup files and a critical objective of software that creates backups. It is also relevant to the design of disk memory systems, specifically relating to what happens when they are unexpectedly shut down.
As a relevant backup example, consider a website with a database such as the online encyclopedia Wikipedia, which needs to be operational around the clock, but also must be backed up with regularity to protect against disaster. Portions of Wikipedia are constantly being updated every minute of every day, meanwhile, Wikipedia's database is stored on servers in the form of one or several very large files which require minutes or hours to back up.
These large files—as with any database—contain numerous data structures which reference each other by location. For example, some structures are indexes which permit the database subsystem to quickly find search results. If the data structures cease to reference each other properly, then the database can be said to be corrupted.
Counter example
The importance of point-in-time consistency can be illustrated with what would happen if a backup were made without it.
Assume Wikipedia's database is a huge file, which has an important index located 20% of the way through, and saves article data at the 75% mark. Consider a scenario where an editor comes and creates a new article at the same time a backup is being performed, which is being made as a simple "file copy" which copies from the beginning to the end of the large file(s) and doesn't consider data consistency - and at the time of the article edit, it is 50% complete. The new article is added to the article space (at the 75% mark) and a corresponding index entry is added (at the 20% mark).
Because the backup is already halfway done and the index already copied, the backup will be written with the article data present, but with the index reference missing. As a result of the inconsistency, this file is considered corrupted.
In real life, a real database such as Wikipedia's may be edited thousands of times per hour, and references are virtually always spread throughout the file and can number into the millions, billions, or more. A sequential "copy" backup would literally contain so many small corruptions that the backup would be completely unusable without a lengthy repair process which could provide no guarantee as to the completeness of what has been recovered.
A backup process which properly accounts for data consistency ensures that the backup is a snapshot of how the entire database looked at a single moment. In the given Wikipedia example, it would ensure that the backup was written without the added article at the 75% mark, so that the article data would be consistent with the index data previously written.
Disk caching systems
Point-in-time consistency is also relevant to computer disk subsystems.
Specifically, operating systems and file systems are designed with the expectation that the computer system they are running on could lose power, crash, fail, or otherwise cease operating at any time. When properly designed, they ensure that data will not be unrecoverably corrupted if the power is lost. Operating systems and file systems do this by ensuring that data is written to a hard disk in a certain order, and rely on that in order to detect and recover from unexpected shutdowns.
On the other hand, rigorously writing data to disk in the order that maximizes data integrity also impacts performance. A process of write caching is used to consolidate and re-sequence write operations such that they can be done faster by minimizing the time spent moving disk heads.
Data consistency concerns arise when write caching changes the sequence in which writes are carried out, because it there exists the possibility of an unexpected shutdown that violates the operating system's expectation that all writes will be committed sequentially.
For example, in order to save a typical document or picture file, an operating system might write the following records to a disk in the following order: Journal entry saying file XYZ is about to be saved into sector 123. The actual contents of the file XYZ are written into sector 123. Sector 123 is now flagged as occupied in the record of free/used space. Journal entry noting the file completely saved, and its name is XYZ and is located in sector 123.