ODPI-C is an open source library of C code that simplifies the use of common Oracle Call Interface (OCI) features for Oracle Database drivers and user applications. It sits on top of OCI and requires Oracle client libraries.
The big change in this release is the addition of runtime dynamic linking of the Oracle client libraries. It was initiated by a comment from Vincent Rogier, author of OCILIB when he took a look at ODPI-C.
One you have downloaded ODPI-C source (and written something using its API, or copied the samples) you can compile your code without needing the Oracle header files (e.g. you don't need the Oracle Instant Client SDK). All you need to have are the Oracle client libraries from Oracle Database 11.2, 12.1 or 12.2 in your path when you run your application. These client libraries can be found in the Instant Client Basic or Basic Light packages, in a database ORACLE_HOME, or in a full Oracle Client install. Your ODPI-C -based application will use the first Oracle client libraries in your load path. More details about configuring the Oracle client are in the documentation. In summary you only need to build your application once and it will run using Oracle 11.2, 12.1 or 12.2 client libraries.
If you want to see ODPI-C in action in a bigger 'example', look at the master branch of cx_Oracle.