Where does the ABAP program run?

All ABAP programs reside inside the SAP database. They are not stored
in separate external files like Java or C++ programs. In the database
all ABAP code exists in two forms: source code, which can be viewed
and edited with the ABAP Workbench tools, and generated code, a binary
representation somewhat comparable with Java bytecode. ABAP programs
execute under the control of the runtime system, which is part of the
SAP kernel. The runtime system is responsible for processing ABAP
statements, controlling the flow logic of screens and responding to
events (such as a user clicking on a screen button). A key component
of the ABAP runtime system is the Database Interface, which turns
database-independent ABAP statements ("Open SQL") into statements
understood by the underlying DBMS ("Native SQL"). The database
interface handles all the communication with the relational database
on behalf of ABAP programs; it also contains extra features such as
buffering of frequently accessed data in the local memory of the
application server.

SAP has three different layers as presentation layer (GUI),
application layer (programs run on this) and data base layer where all
data is stored and retrieved from user driven conditions,commands
given by end user programmer through presentation layer.