The $ALTIBASE_HOME directory contains various subdirectories that store important Altibase files including configuration files, data files, log files, library files, sample programs, and trace files. Key subdirectories include bin for execution files, conf for configuration files, lib for library files, include for header files, logs for redo log and anchor files, and trc for trace files recording the current Altibase status. The directory also contains utilities like Audit for data replication consistency checks and directories for archived logs, messages, and database samples.