In general, a data type overflow error is when the data type used to store data was not large enough to hold the data. Furthermore, some data types can only store numbers up to a certain size. An overflow error will be produced, for example, if a data type is a single byte and the data to be stored is greater than 256.
Other common overflow errors include overflow errors when an application requests 64 bits of storage but the program can only provide 32 bits and overflow errors when a variable is not large enough to process the value for the size of a SQL Server database.
Overflow errors generally result from software bugs that did not get ironed out during the development process. That said, overflow errors are not common in successful, mature software products as the errors have been caught and fixed in earlier versions.
Idera’s Knowledge Base discusses a number of different overflow errors that you can experience with their SQL Server database products and the solutions to these errors.