The main table that contains this information is FND_CONCURRENT_REQUESTS - you will have to join other tables as needed. The data in this table is purged when concurrent 'Purge Concurrent Request and/or Manager Data (FNDCPPUR)' is run.
Query FND_CONCURRENT_REQUESTS table for ACTUAL_START_DATE and ACTUAL_COMPLETION_DATE (join it with FND_CONCURRENT_PROGRAMS AND FND_USER tables).
How To Check List, Start And End Dates Of A Parent Concurrent Request And All Child Processes [ID 751438.1]
Or, Google (FND_CONCURRENT_REQUESTS, ACTUAL_COMPLETION_DATE, ACTUAL_START_DATE) and you will get many hits.