Key Items are items that are Soul-Bound. They cannot be dropped, nor transferred to other players. They are useful for progressing the character's storyline, which often requires these items to proceed.
For example, to progress from Story Mission 1 to Story Mission 2, a mission-specific item would be the key to unlocking that second mission. although missions are stored in players (whether they be completed or worked on), key items will help to open up new missions to the player.
When advancing to a new class, a very special Key Item is required for you to be able to complete the transition. The item is obtained when special needs are met, and also when a test has been completed.