An Emergency Trial might suddenly occur during your quest.
The trial is activated when you receive orders from an operator. Trial Objectives will often involve defeating a certain enemy. Objectives can be checked by going to "Main Menu" → "Quest" → "Quest Info" and selecting "Current Emergency Trials."
You will be rewarded upon clearing a trial. If you don't have any space available in your Inventory or Storage, or you have maxed out on a particular item, the reward will be sent to Temporary Storage. If a Quest Objective is accomplished by clearing the trial, the quest will be cleared, and a Telepipe will appear to take you back to the ship.