Mission objectives are specific tasks invented by the mission designer for the player to complete. In game design terms they are usually associated with triggers: when the trigger is fired, the objective has been completed and the consequences occur.
snYpir wrote a very good tutorial "How to use objectives and init.sqs" and I'm not sure if its knocking around anywhere. Also read his Briefing.html tutorial, if you can find it. We are in the process of recovering as much of the old Editors Depot as we can and some tutes are already available in the new Editors Depot. Others are on the way.