What does the bounty hunter mean by unique champions?

To give this a bit more ease of understanding - think about Rengar's (3rd? 4th?) most recent Bonetooth Necklace iteration from the Assassin Class Update.

Rengar gains increased base attack damage and increased bonus attack damage for each unique champion killed - notably capping at 5. Once you've slaughtered everyone on the enemy team at least once, you've got the most possible benefit out of the Bonetooth Necklace.

The same applies for the Bounty Hunter Mastery.

The last thing to note (although it is generally obvious, especially at this point) is that "Unique Champions Killed" does not equal "Non-Consecutive Champion Kills". Sounds similar, but honestly before reading A Koichi Pose's comment I was pretty confused about it myself.

Hope this helps smooth out getting Koichi's point what little ways it can!