ODBC (Open Database Connectivity) is a standard way for a piece of software (an application) to connect to and communicate with a Relational Database. Without it, every application would need to know the specific technical details of every different type of database it wanted to talk to. That would be slow, messy, and hard to maintain.
ODBC solves this by providing a common set of rules (an interface) that both the application and the database agree to follow. In ATAR CS the context is often a web application such as a Content Management System (CMS) or “web page” connecting to a database.