I just did something similar not that long ago, so here that is...more or less, taking into account and making a couple of alterations with 5e in mind.
While I don't so much consider the use of "tiers" as such to be necessary/outlined for the game. But it is a handy way of breaking down packaging and/or levels and standards of what a challenging adventure might entail. I would prefer the "ditching" of the 4e terminology as much as possible.
Adventurer "tier": Lvls 1-5. You are beginning your quest for fame and fortune, seeking out, taking on (or even becoming accidentally involved) local troubles and exploring strange goings-on "close to home". Get your feet wet and yourself familiarized with the rules and expectations of playing a RPG of fantasy adventure.
Champion "tier": Lvls 5-10. You know how to adventure and survive whatever perils the world wants to throw at you. You are even quite good at it and rise in power, glory, wealth and fame (or infamy) that few attain. You traverse the realms more or less at will and venture into regions few ever tread (inhospitable terrains -deserts, the artic tundra, deeper beneath the earth, oversea, undersea and aerial adventures.) Bringing you, the player, to a close with the PC achieving "Name Level" (obviously, this requires redefining name level to just be 10th, across the board, and that's it.) The character retires as a happy wealthy Lord or Lady and the player can make up new character...orrrr keep going....
Hero "tier" (i.e. you are a "Hero" in your own right, as opposed to a "Champion" which has the connotation that you are fighting for someone else)/"Name Level" Set: Lvls 10-20. You become Lords and Ladies among men. You develop and build your strongholds. Expand your territories and manage the trials and tribulations of your domain. You venture into realms and traverse the planes beyond your world that normal men (and adventurers!) fear to tread, or even know exist.
(even though BECMI already used this, it does follow the Adventurer/Champion/Hero motif better than any other tier title/name) Master "tier"/"Epic levels" set: Lvls 20+.
[EDIT for Kamikaze Midget's thread] I'm actually going to borrow from Stormonu's post and use "Legendary" here. That works well, I think...without having to re-use "Master set." Or just the "Legends" set/tier/what have you...so...[/EDIT]
Legends "tier"/"Epic levels" set: You are Lords and Ladies of/beyond the Lords and Ladies of men. You attain Demi-godhood, essentially. Take part in (if not actually cause!) those monolithic battles among the forces of good and evil that expand across the world and multiverse, easily venture to other planes, take on Demon Lords and aiding (or assaulting) the Gods...and beyond.
The "Advanced" hardcover rules manuals would contain everything necessary from levels 1-20. With 20+ play left for an additional/expansion book/module.