Original: At this time, the Countess sees Cherubino's commission, and notes that the Count was obviously in such a hurry that he forgot to seal it with his signet ring (which was necessary to make it an official document).
Simplified: The Countess sees Cherubino's letter about joining the army, and she notices that the Count was obviously in such a hurry that he forgot to seal it with his signet ring (which was necessary to make it an official document).