Your progression keys auto-upgrade, when the DPS of your equipped gun gets higher, up to Epic.
Key / Rarity
Completing a raid tier on Epic for the first time will drop a progression key for the next tier. (Normal Epic drops an Advanced Key) Progressing key tiers not only makes it more challenging, but also drops much better loot!
Replaying Epic+ raids will drop you key-shards, which you can use to craft Legendary and Mythic challenge keys in Expert or higher raids! Challenge keys are single use. You can use Raid Mods to add special gameplay modifiers to challenge keys.
Boss keys are a hybrid of the above. They are single use but scale with your DPS up to Epic and can also be upgraded to Legendary and Mythic using key-shards. Higher raids means higher chances, more experience, and phatter loot!