GUI = Graphical User Interface, as opposed to a command-line user interface
(R)DBMS = (relational) Database Management System (e.g. systems as being built
by Oracle, Sybase, ...)
PSQL = PostgresQL, a freely available DBMS, the outcome of a large joint effort
to make available such a free RDBMS (RDBMS = relational DBMS).
(www.postgresql.org)
API = Application Programming Interface, such as the C/C++ header files for a
library or VisualBasic for the MS Office applications - a way to hook into an
existing application to use the services of that application and/or extend its
functionality.
Cheers (and apologies for the acronym flooding...),
Oli