ODBC is a standard set of calls, which is used for connecting and interacting with a database, and defines a standardized way of interaction with any kind of database.
There are various kinds of databases available from various vendors, who normally have a native (proprietary) driver for their database. ODBC is a standard that was created to make applications independent of the database, making those applications portable to other types of databases. If an application is developed, which uses only ODBC calls for interaction with a database, the application is independent of the kind of database being used. The database vendors supply an ODBC driver along with the database. If an application uses only ODBC calls, it will be able to interact with any database, for which an ODBC driver is available, without recompilation.