Business Application Programming Interface or BAPI is a must know lots about subject. Developing in SAP will inevitably involve using standard SAP documents like the Purchase Order. A BAPI will help you do your changes to this standard SAP document... using the "programming interface" that SAP have prepared for this.
So what is a BAPI ? It's a function module that allows the execution of changes (or create) of standard SAP documents. Where an error is found in the data you want to execute a change with, the BAPI will inform you via it's (function module) interface. Hence "Programming interface".