A champion permanent is a hextech crafting item that can be consumed to add the champion to the list of champions you own.
Upgrading a champion shard into a champion permanent automatically consumes the permanent and adds it to your inventory.
The only way to actually get a champion perm (and have it in your inventory without it auto-consuming because you upgraded it from something else) IIRC is via missions (generally low-level missions that give you champions for playing the game) that give them to you, since the reroll feature no longer exists for champion shards. This is probably because champ shards can be used for champ mastery upgrades, so having the champ permanent in your hextech crafting inventory would be pretty pointless.