HL7 messages in the hl7_in_queue table are processed by the HL7 In Queue Processor openmrs scheduled task. Make sure that task is started and running to process hl7 messages.
For OpenMRS less than 1.6, make sure that the scheduler.username/password runtime (and possible global) properties are set properly.
For OpenMRS 1.7+, no username/password are needed. Scheduled tasks are run as the daemon user.
(Successfully?) processed HL7 messages are moved to the hl7_in_archive table. Here they remain for reference purpose as there are often cases where having the original data is invaluable – tracking down data quality issues, troubleshooting problems with ancillary systems. A commonly suggested best practice is to archive them from time to time if the size of the database is important.