Since a BAPI can be used to e.g. create a Sales order via a programming interface (no SAP user to supply any data), calling this function in another system is the key to speedy processing. Most BAPI's are therefore "Remote-enabled functions". Applications like the XI (used to be the Business Connector) or other SAP systems can use the RFC mechanism to retrieve data (e.g. RFC_READ_TABLE or a suite of GETDETAIL functionality on SAP documents) or even change or create documents in the SAP system from an outside call. These calls can be prepared in Java, C, or ABAP, or effectively any language.
RFC calls require an RFC destination which can be found in transaction SM59. RFC connextions come in a variety of types and when you dig a little deeper into this you will find you are stepping out of the SAP comfort zone. RFC connections of the type ABAP connection (3) may look familiair, as they simply link (log on) to another SAP system. Have a look at the settings for type TCP/IP Connection (T) and you'll find settings that have no bearing on anything Abap or SAP. Connect to the outside world !
Monitor errors in RFC calls with transaction SM58 - "Asynchronous RFC Error Log".